Chapter 7 Exercises

Clarifying the Concepts

Question 7.1

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Question 7.2

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Question 7.3

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Question 7.4

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184

Question 7.5

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Question 7.6

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Question 7.7

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Question 7.8

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Question 7.9

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Question 7.10

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Question 7.11

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Question 7.12

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Question 7.13

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Question 7.14

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Question 7.15

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Question 7.16

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Question 7.17

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Question 7.18

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Question 7.19

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Question 7.20

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Calculating the Statistic

Question 7.21

Calculate the following percentages for a z score of 0.74, with a tail of 22.96%:

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  2. gY2aFqjozPvoMtO1DaDjU6qIFvTQmvOGdg5P9V8Wa1uxAC+xQqMKGfLfUfy7uSvD41Fn8+Yi1wSx6MJrNC8epW24nbm3oNHH39mq3OEzhCcYPJtgbpLCPOmg3YY=
  3. OtvBDyQRthiZsWVZJgLg9T4OTvH94gLbk98kTNqCYjbKa+OME7NACT6654vtBztZEKbSRsUcoh5r3e4skt9KSOrLpuX9FVqXQFoe7zap5NIki6Ul

Question 7.22

Using the z table in Appendix B, calculate the following percentages for a z score of −0.08:

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  2. iCi/X1ztWYhxIXx1QxsFpGfy0P1YOjI3F52GL0r6cblAGmh/ocWlMSlT+QY=
  3. Hr/AlR5m0JkFxeELXM19NHcNOFykC4lzYQ5lXr/yWGJ5gi1Ob715VduLa5obxQ/r7FIDsmQdqJs6w3QM

Question 7.23

Using the z table in Appendix B, calculate the following percentages for a z score of 1.71:

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  2. iCi/X1ztWYhxIXx1QxsFpGfy0P1YOjI3F52GL0r6cblAGmh/ocWlMSlT+QY=
  3. Hr/AlR5m0JkFxeELXM19NHcNOFykC4lzYQ5lXr/yWGJ5gi1Ob715VduLa5obxQ/r7FIDsmQdqJs6w3QM

Question 7.24

Rewrite each of the following percentages as probabilities, or p levels:

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  2. 64NgrorZ0LKJACuygF0Ak5NgVq4=
  3. PIK5i2+6aZrL+WbH8wdcciK1tNs=

Question 7.25

Rewrite each of the following probabilities, or p levels, as percentages:

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  2. Ec/9N75IXojz7kDtDsDoUK0XTsc=
  3. xvrtAcwmvSlRmvDLKGf106E7Y3g=

Question 7.26

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Question 7.27

For each of the following p levels, what percentage of the data will be in each critical region for a two-tailed test?

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Question 7.28

State the percentage of scores in a one-tailed critical region for each of the following p levels:

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  2. DDUDmqRgVaWp+UNJqD5qt0pY/Z4=
  3. vR0y5+kqxtLGJi0rRiL+NHAu2w4=

Question 7.29

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Question 7.30

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Question 7.31

If the cutoffs for a z test are −1.96 and 1.96, determine whether you would reject or fail to reject the null hypothesis in each of the following cases:

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  2. NgUw4f7A3n6vlswUDskb/ZN8TI872ICRAVbmiTcMP33Drr3L
  3. 76HOr5qDdenrfDPOqpS+iyGZliWxWtr5BUkR14LyhuEViYFglw95pNMdX/jXP/g7fBiv6RotggkgzCNhzCsr94DiplepqiDGpJIA05lowDU=

Question 7.32

If the cutoffs for a z test are −2.58 and 2.58, determine whether you would reject or fail to reject the null hypothesis in each of the following cases:

  1. sz1Z9dktUBonHJ2F+3evPDjnwkJGN98P+Rm19QoRgPAp85zI
  2. Lq2bB9uHrP70VrV1TBGJQFqZYTDiajU+RwGfirzCWBtGaYpm
  3. IEimPWwLAunLLih4icVQ5ebykPRlA7TzD/7UERLMdli+lMn4ZqtSXjJZivnydTfLlD/RtUPuZUUiPqV/LK7YSA8t0BX3x7HmC54zLn6ZVYBAftTutyjnkIYo/SaC0a9TEIZ9YA==

185

Question 7.33

Use the cutoffs of −1.65 and 1.65 and a p level of approximately 0.10, or 10%. For each of the following values, determine whether you would reject or fail to reject the null hypothesis:

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  2. T1a7+RqO8AouAEXVg6ZO8qq7w8fD4i4OGH2SeVhjpD2O3Fe8
  3. MhGmNprXnjbrHu9vAfZ5Bf54RDx81Gu+P5aaiJYOFSaXQ27BFWOKlQsTkaGT3bDxwwk/u/pD9zl31sbDd632+3WQKJobRJP6

Question 7.34

You are conducting a z test on a sample for which you observe a mean weight of 150 pounds. The population mean is 160, and the standard deviation is 100.

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  3. efjnXtdDioKKUND/uxt2YlzPPK8S+sAABGVIK+GCC70TXSHD2ExODsDzi8loMrpQPszOHjRhK8Zzgvlo

Question 7.35

For each of the following, indicate whether or not the situation describes misleading data that the researcher may decide to investigate and potentially discard.

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  2. sbFVQOzsdT4nPmxtC38zzAp6ZnV+JEOiCyOl7n+W+KmE+o1n7u2HWzjL9HUZaGt8D16bo5BjkT+cX7pO4a96aYmdObSJ/2iaX/2H4BzqsEEf96jcO8X4x2pf8KAZBn0xgGMNVlM9oHgB4jGGWLln0Z2NmDFusgwe0jeYgoVNNVK1B+FGpBA0YLBli7ZyFj/mEDPMbNeCtyXjch36a9ivs+Zb2Mil2qE962Vto4aywJzrJY/YRlWwlKobTiFrLnUDyf2cIMrC1+sTTqnDsoE2xP0bUZRWVT4hl6eOq+PYG5+iaMkwtJgYt7FVQ7nJ2GXzEITYDUK0gl/VEdTbVTA/KsFsg9T+4Py5uuhli0XxAlxWmEJgYpIzH/6Rb/yjEDPpdAmatrO/wvo=
  3. A1mzMmv3+rOC4R+Di3LrQdkOJSsEQjJ/Ie0Ysq6vUptQqmsu1oDqa5I31R9upntCZR68dim54Dm5O2/LcximTZdX1cxnkUQG2kSq0Np/f3XitKKhYM38cj++pN9ZZo8+OrVsOHxLD50YE8CtFgc2fnYODFTTs7ibVQY1daAG9zIbiVB7Hxl03fmxgpon+mKJNnCsOJaJIx+o3uO/b74LeZaMuhNLNmA9tettSBgMpJzViITmKnis06WvdMnRONdZeLeCURjDbmvN+vTQ+rIsF93AgNYIiSz4FJCJdTdvuEkFVLu3Yy+1FXlaXQEoAZQ1oT48NeemuYsSMZ8KqYN1sD76cDQ5Qrq8aOgZuTjJMyb12KZfsx8IUBl+x0cCzLqh9VzYFIU7rB86Q0VBe8Wl2WT7b4OnmjNsAES4EhfNt5DMwhlhZ9HyYu8CO/SuEUYzXdnArw==

Question 7.36

Assume that the following set of data represents the responses of 10 participants to three similar statements. The participants rated their agreement with each statement on a scale from 1 to 7.

Participant S1 S2 S3
1 2 3 2
2 6 7 3
3 3 2 5
4 7 6 5
5 2 3 3
6 5 5 6
7 9 5 4
8 2 3 7
9 6 7 7
10 3 6 5
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  2. JUDixgl7AjQQQba/s7UXRKjdMIYKcivIk6vHmaxTc23aMyb3hytxZTY7bjgnKOPVi+AZyZkyr0vpFTpmjs/XrW1r/4g+1Ilpnxqw2wIKg4HS2zEu4gvrbGzafxsqRmjK/wgMBRcP9Kk4ah//YDS8Wma0+yb//gXJ9RUZNeC3I0BrkkJO3TrRaDSLyJsw2P2mjiOdB4J4nyII6DuBL7VVOkLoOywBb0CnLJU0vcIZQmDJx2xtVkA1Cw==
  3. LLYPPSIWdC6wjl9A3ki1nNoWaJgCuIYCLjUZ1UAlvjydny1ezj6CMnEDsM+u0fEcnJZ8ZgVqPB0fElSw0QX1+i2TrGu9pDM+pSPD0I2GeyohlZ9r1t5Cxfq5cdTWMS8A4w9n838N65pfCBqmFkxE4Q+xaPHHCI50n7DiyRL5T5OTBLrFhdka5e9cXwIqxkDec3XL0/RzwfM3c0RjA0PuFh+aEym4mnu9tBAYJKVZRvEQes/6O7J7DeKXkfcFgKZOoAB6QwApiyg=

Applying the Concepts

Question 7.37

Percentiles and unemployment rates: The U.S. Bureau of Labor Statistics’ annual report published in 2011 provided adjusted unemployment rates for 10 countries. The mean was 7, and the standard deviation was 1.85. For the following calculations, treat these as the population mean and standard deviation.

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  2. X720Ih3xXtIyv/ptye7ys+ASkbdIViyT4t/wj9FolxW5SXQiBReUaeyoq/iThIS6nvpVXuXRfv6ASCfbYT+33Bl0twrg+/oLYABjPOCQDQnSkOe1zbjvxIrkfPEq7suoOmd2uSeTapMfk7hyYtfusoCexH/5BedDb2RcxYwRJahDv7S7fheALE/3Vy89BMnPvnnpwgNc5Gl93QyASnbGXOxfcSxzLW4KX/fNG9zT9fQ01koG76iSuBFWE8aZUrdupvvQBf00mEBwsYKJJDtHgg==
  3. z4fIOx+vsLKXRUCRKaSAVDZo5v8JeNX9/JFJkLjA7A06IFn1fKm9bKD4+DqcX/b2f1/wm0Mmc/hchEZbUefw6l3vqAgFNqP57u2DO9Nvc5vd9hooa2wv1nScKGmPfaq3kLlSuXv0bOSVEC86okVMvFNRe7pdIzF11/z5FU1WPrFCbpSHo/P/VBRFLouWwfYK3nBIu84rVlpZdjz2uUmkcgNDoCCV+ce7CqAtEda16SyktvQTDkk97wCdvXDXU7omy51p3KIqiideDgD8e9WdVA==
  4. D57jPWwjFEoJtg35yXSQoEq3ghhm5PLKKIr6B8DMqdw+5m2nQethWzZpuFB4/BKxCnaSqHGmEXPmErdIKJFMjCTpfepchREphhGGAu5InO7SImytgBLGdju1ZjR9UwUjp/qecnDQpotZxXaL3jWqX2lH2FwXy7jmsdUpZTRebsqaUvU07ZZ1E9WxoK4qGkKSr3Elh0VGu/h1OtYSBuDcZ+7gECWabYpNIY0FHwOtAeSQxO66+Mp7lA==

Question 7.38

Height and the z distribution: Elena, a 15-year-old girl, is 58 inches tall. Based on what we know, the average height for girls at this age is 63.80 inches, with a standard deviation of 2.66 inches.

  1. xfyBOy4SMutHnfN1RuLQhHKsl0ZTiLpUgDBqey7108a+B+bljywIDy5yil4hURzTw/qHFfcD5nE=
  2. 6nsTrn7NPpH1F3Tx/KW3MVqTqvzBdWD5tdjH7jD5v4ICVYwaQGlqDAG5UJjcLsqOHxbHH0+p4NXZlAgjbrzGVw==
  3. eSoWx7l4OpLs1o9FJTBMkAnxE8dBeiNLZzj5whvzwdWm3eSO8j46sMOHPQ30cWE89Sdj4gGdrSk=
  4. XqYF4f0qSDQo/Mz23rmK7sPXXAkCdd4wZ55lY69EAONqO8IWds6HMJ89YOjTegt3oiQpHAmzq0RKJg2dIJm5eCIFcU5ryDKzApaXCw==
  5. DHiBEO3wPbi8YEc30EFdvkh5h5M0yiEOfIOGC/mBISJ1qJhyrfvA3MW8uEs07xB42e/kJYjzTscM43HJn9dccLoyy6RwDsh1FtNaiehTSipajHjsT4FAEPT5Tng=
  6. hRpZ9icFFl0zvT1cQLuhJVCSXIEkkgidF+KPGFBoR/atWaHGNktP8g8usj2ibhdY3TCOJEdVeS1626B3wgwnbKAIoIrLN21rfds7CNm01a/z/S51D+JDKDUDAr1pjQSs52tnrA==

Question 7.39

Height and the z distribution: Kona, a 15-year-old boy, is 72 inches tall. According to the CDC, the average height for boys at this age is 67.00 inches, with a standard deviation of 3.19 inches.

  1. Z5QAjjIrMi6x24xhqN5AagwVAoDyL2nn5V8OuN3MePYyaHg6nyGO/D9KoF258w0nV7QKUA==
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  3. 5Qe0nTlbFUQ3FXcGh02Aep82ztZtJLGclFmG26heZ110vtznwySHvDtV8uWu5/2WQ+B1a9Ld5LFInSaykB19JYxK8m4pVWs7
  4. jCei2mpItR+ThzvLub5tPSs9BSKnXDd58MlsuU6Kw9/WplYMYPYaaYfcKcXMSYDLTImr//rjTQwuMT/fJGSXi2u34al1lPIUOs9k88OZt83tAJhtOH+HYeDzNXXEHQHpzowR5Q==
  5. Z9fjBbAIG2EzSsQnoIShXhlFfv/UIAi7Ccd15H0ulTQACbkIcFR9eleScHeBIZXcJtbDtvG70TL/vRH04KKVplHVGmFt6KSBBfweonCjZY+qOwnXCmIa4n6hsXUp0LUBzz5TmUCXaLES1I0tszUB9LsTk7P9BQirf/9WSwVWJB+n37CwjV6qK8+qlU2j6hTQZF2WaeUDkVFc4xpMObUURqV4K6bmoLkDehvfBnOgtVKwokushKeSIz3Yuch1kMpVeuqxt2319OHtHz+HdhcqjYFUq/t6tO3T+R59HA==

186

Question 7.40

Height and the z statistic: Imagine a class of thirty-three 15-year-old girls with an average height of 62.6 inches. Remember, μ = 63.8 inches and σ = 2.66 inches.

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  3. tgYL+Ct4mF5xGQwg66je+z15bpZR/HQnadqsxjRirUFoaXrhzkPp96KzzGOYAZZmLJ2B6k0L1EekT5ku

Question 7.41

Height and the z statistic: Imagine a basketball team comprised of thirteen 15-year-old boys. The average height of the team is 69.5 inches. Remember, μ = 67 inches and σ = 3.19 inches.

  1. VQbmj5pJzs5bpggK0Di3jCBoIYk2aUgP/yKDmMngd2cF7eaXM3zbdvyaIYEZwtjjYCW1aQ==
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  3. tgYL+Ct4mF5xGQwg66je+z15bpZR/HQnadqsxjRirUFoaXrhzkPp96KzzGOYAZZmLJ2B6k0L1EekT5ku

Question 7.42

The z distribution and statistics test scores: Imagine that your statistics professor lost all records of students’ raw scores on a recent test. However, she did record students’ z scores for the test, as well as the class average of 41 out of 50 points and the standard deviation of 3 points (treat these as population parameters). She informs you that your z score was 1.10.

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  3. jKv9UI+2IbXjJODzSlRy1fwiXlLagb8YyZNDdRe1FssoyAj+m0HIR8m5gOPkhIKERnrCDQ==

Question 7.43

The z statistic, distributions of means, and height: Using what we know about the height of 15-year-old girls (again, μ = 63.8 inches and σ = 2.66 inches), imagine that a teacher finds the average height of 14 female students in one of her classes to be 62.4 inches.

  1. W/MJ8X5YGQXN0tEoSh7fpDYtJj0d+XwaUzCFT/FkXrNspeX1PEUzbt1XIXHKpmKJuDTu/dgZytZMrdYNgsbqZsIYCn/1kZWTkd+j075OCbStLnDQzBLVZm+xJinjydpr
  2. 7yY5oVbxanAurRXsHkmTHP/Kn+qzUKI8NyQPjTg5FF6Jce//R/dIuTpy19Wiz6cBZl6fW2YBVY9EljkNLEL+/mehiCU=
  3. VN7u0lR3OzuZYFGsDMayMnynyh7r9BNsvHJNM9hZhy2tLdS+uL6lmhPoXL3NjmcL3SAcebIMuMHucZVwyfzez3V5gSr2yBgYGhQ4G/gxeDfaBToXYU1hEGlsQmeI40WBqnl6XP+94zjRcpdIgSMF3EbWS9ZQqaa4viWxLL/T8QIOJxzeSd5yuw==
  4. Ic1efRg73R3TQtuOqDap0ylrMYRwjFmTpLR53mH1G2mnBCBDa8w8mwOfaMyYzVxKgu29jaoBcI7Yy+onxxhYOddbhASOhuAYTLDqp+o6Rm/Df6Xmn+2YEHq/qcIJhGvNQRK1Qg3Z1IC+c9Y5
  5. 7YIhVTYwxhie6WHqFPcvnzZHdYMOZCxXCLENqmqvoRbm53ocXscNRdBFlrfdZ8849U1tKgD+yFtNQrbhdkeUFdB6X0rwybL+2pttvX4qdLnx7BL7XxKfH9UU8h8FwNuFhalSs1hTabHl3E0VQ59xxj1lQ57QwF4gxdjB0LsFZCL2qkNuw1OsHBXPlrF3aL9GX/XSg9ebePY=

Question 7.44

The z statistic, distributions of means, and height: Another teacher decides to average the height of all 15-year-old male students in his classes throughout the day. By the end of the day, he has measured the heights of 57 boys and calculated an average of 68.1 inches (remember, for this population μ = 67 inches and σ = 3.19 inches).

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  2. 7yY5oVbxanAurRXsHkmTHP/Kn+qzUKI8NyQPjTg5FF6Jce//R/dIuTpy19Wiz6cBZl6fW2YBVY9EljkNLEL+/mehiCU=
  3. ZPmNP2sRHU/N8X5KYzpalfUo7GNRG35JAajNqFEDFcbw2PjNKl6eOkHNJblVJYigFGKAZUhlBQvUFtNInsgNTYQWM7kzwNKR42c8N3Ixd/WFHgsR0gdD8GdYz/s8eXLMwHtzjFT8Mdw1WMEafoitkw2phTClBTREObejANHOl2MVEpnnBnrjWnZwVlvYU2pYkNgaUG15DK8=
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  5. oJhE6BKGlX5eScFjODeJMXGYLhOBL/gUmtZenSyR+Xf9vJ80Me2Gn2h7Igx4WVYte8ZynuT2Vpf7nDMk231zUa3QbiBhkn9tmbgmygzy+MqqNwzm2jccFITRhFg=

Question 7.45

Directional versus nondirectional hypotheses: For each of the following examples, identify whether the research has expressed a directional or a nondirectional hypothesis:

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  3. N8aZ2uDwHECK8ng6bCV4PUcHSufxfOyK2Gkj8ER4bt4eXJZGn3PZqGXXG9Srt12h4ULapm9EfxxzLCATK5tf7sw9Eq9RUm9l3wFytmdT2TCqt125LLa6xOESAH1Rpg4B8ucgh88Erz4WaD31QPzK5kKYBZoZpX//5WDkr5PUY7y98uGEbDiDDTU5mL9QPvdbgd1Xk8lGAy6oRYPPFfuf6AF7Z5hDJEw06LymIvi5RI5fIUTGwvr+zX0653gYwn69xl1fuq0e8xbOviOnux5ORHAAVqugGlTFV8hCtVS1CPbLk3WStHSLVHMe0jI=

Question 7.46

Null hypotheses and research hypotheses: For each of the following examples (the same as those in Exercise 7.45), state the null hypothesis and the research hypothesis, in both words and symbolic notation:

  1. Pj/5yhETIKBk6yOPJPkPfIO1BhjMi6pgbxgQiJoYyg5hE9xLidV/RX44LsVbi+vVJT90rE4QfenMb/m6WSIFnaDHqErzVwt2DH1TcLaCd+PdEjPgfdBT0IOenjOqZXlz+N/GEm3Y7q7Z+2pM9IUTVZbhhw+t8GB5dq/tAgKQiUjl9AOHnQeVLNxLEifvNbONiQ8i0ujzxIRm3WDj9OSKm+ERb0Z90a818vGLBtT7EPO9t8i1+2Afp+mk5p2AwntXq26vxpzbZtC69kFHSkATj+CoVWAlNgq1sijP/sQL8EuYqT/PINRwZ0Yxy+TFW2VpK5o9Jr/FypQJN2bpNQyoyHr/MoU8oRAB
  2. AfiCefPDhcCq6wlxlmkeFRiiUzEhG3q2nx4KgVbgiicuwW0+pz9Z6lVIykQbgKM+i+VCzsDxkg3pFePWRiAXOzQZJDIYRBkkJ5oRgscUl6Nh5ldb9drf6j0S/KYYXC2wPxG39licSyBjOGjt4S/oqulr3gPy/8ylQk98yJz+x4jl2ViGhWotPq0Pu48VJ7l0iJBPBN0uqp/ib9d8sT4sVHt9K9xlX4PAt/wjwjFMB4UBgMdcR8PrW3ekAQs5wN0wzEFB3qU1lF59zdDLgrrv0t0ODTY1K8QssWV3WzmKyGixx3RZ1mYnliCefBKx4IIe193RRg==
  3. N8aZ2uDwHECK8ng6bCV4PUcHSufxfOyK2Gkj8ER4bt4eXJZGn3PZqGXXG9Srt12h4ULapm9EfxxzLCATK5tf7sw9Eq9RUm9l3wFytmdT2TCqt125LLa6xOESAH1Rpg4B8ucgh88Erz4WaD31QPzK5kKYBZoZpX//5WDkr5PUY7y98uGEbDiDDTU5mL9QPvdbgd1Xk8lGAy6oRYPPFfuf6AF7Z5hDJEw06LymIvi5RI5fIUTGwvr+zX0653gYwn69xl1fuq0e8xbOviOnux5ORHAAVqugGlTFV8hCtVS1CPbLk3WStHSLVHMe0jI=

Question 7.47

The z distribution and Hurricane Katrina: Hurricane Katrina hit New Orleans on August 29, 2005. The National Weather Service Forecast Office maintains online archives of climate data for all U.S. cities and areas. These archives allow us to find out, for example, how the rainfall in New Orleans that August compared to that in the other months of 2005. The table below shows the National Weather Service data (rainfall in inches) for New Orleans in 2005.

187

January 4.41
February 8.24
March 4.69
April 3.31
May 4.07
June 2.52
July 10.65
August 3.77
September 4.07
October 0.04
November 0.75
December 3.32
  1. vXE9vHpjjKtXBU9MKfm8SDxtaMZD7XWUKmueFnTe1TJ9bvWBu6eHHal/jIci6y1SwuTVn71huMOcQ8pGGlNrZI6KRB/1mU3Xk7nFJKRZ/PMrlaD2kNFxdkjDdpw/t5QUPvDO5gmNo0Dwh0Eh3+bNnvjXaCxhquSNTsjtsO/brKDVY9beex7sWS0UN0DzaP4iHl1M0fN9hnt0ZpW9M83DwxXT83iwcg2hynp5lGKoYY5+pAGL1epL7fPJkpvOAiNmU6e8uKQX+8wQ483qR5UbTw==
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Question 7.48

Percentiles and IQ scores: IQ scores are designed to have a mean of 100 and a standard deviation of 15. IQ testing is one way in which people are categorized as having different levels of mental disability; there are four levels of mental retardation between the IQ scores of 0 and 70.

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  3. h3er4i9WbOJJ4DhdYBeRz/deVA3YIgqw8qiJTNzb3F+6kbQU0ip/+Ins1hWxOKTTkjrSv/+c0gDZDNb+v3AnugbWSJJ9+MfD
  4. wIQce/2tM7/nh7ms/E1yiaXFa+WcBGUPCgb0+L6KgdcdwQk0LTnqfk2HgjQDcswQCKJFiNv1tlCZXvbZ8HxfzmVTC76K5aokld8IS3FnlOrfowVCpihFtyFan/I4q3rveJFJocypu1HG9vFxoj59XyX6OJILEoUG9WUjt2Pqxo4ml1Hj

Question 7.49

Step 1 of hypothesis testing for a study of the Wechsler Adult Intelligence Scale: Boone (1992) examined scores on the Wechsler Adult Intelligence Scale-Revised (WAIS-R) for 150 adult psychiatric inpatients. He determined the “intrasubtest scatter” score for each inpatient. Intrasubtest scatter refers to patterns of responses in which respondents are almost as likely to get easy questions wrong as hard ones. In the WAIS-R, we expect more wrong answers near the end, as the questions become more difficult, so high levels of intrasubtest scatter would be an unusual pattern of responses. Boone wondered if psychiatric patients have different response patterns than nonpatients have. He compared the intrasubtest scatter for 150 patients to population data from the WAIS-R standardization group. Assume that he had access both to means and standard deviations for this population. Boone reported that “the standardization group’s intrasubtest scatter was significantly greater than those reported for the psychiatric inpatients” and concluded that such scatter is normal.

  1. 3YrTkyMucJ5eaZLQlWkVo96GPdLMxWwJSxqZyini3TfTMq+eP2YvL8d8y6El0GVz
  2. Hh8obpa/tyVctRH8ymcbGxH4uU6md+IdtSNS8sZag/FMD7tJZIMljlT4bemV5vDZwqZzYS5B805QlaE88ssn6LiLhkQ=
  3. 5VjhWnTbi8yrhlZkVr1Xgn3umW4uolddSfl8FiKcedfHgwgu6IQArFR4fl83BNVC8IJA3GDQAZwr5BJc
  4. Tk+6f5XJGkUjzsVlBvEipPJnTsdQw1649JpVVQXxWlMNuBs8Q20F2M2CQVGGevMgC3g0j/7+6rjmYFE1YOibfqOV4khxG8HwQwhUnowcTXOi1lcJW4eLaYj/E7O8PTYnuKJ82Q==
  5. DBjjzHW6guG5faY4/TPfC9vcyphXVnlG3ZqPZ70X45jX3itD6fWPufr4BFNoi9GH4l593R1vOVvod4uHk1QobTaSMah6XvWOstw+fQ==

Question 7.50

Step 2 of hypothesis testing for a study of the Wechsler Adult Intelligence Scale: Refer to the scenario described in Exercise 7.49.

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Question 7.51

Step 1 of hypothesis testing for a study of college football: Let’s consider whether U.S. college football teams are more likely or less likely to be mismatched in the upper National Collegiate Athletic Association (NCAA) divisions. Overall, the 53 Football Bowl Subdivision (FBS) games (formerly Division I-A; the highest division) had a mean spread (winning score minus losing score) of 16.189 in a particular week, with a standard deviation of 12.128. We took a sample of 4 games that were played that week in the next-highest league, the Football Championship Subdivision (FCS; formerly Division I-AA), to see if the mean spread was different; one of the many leagues within the FCS, the Patriot League, played 4 games that weekend.

188

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  5. dbQPn5JN+yHqXtSgqT45t/M7suk5WnacXtSdjenxAr88WY/H5gz1KTgrox15fejfCnw4yg==

Question 7.52

Step 2 of hypothesis testing for a study of college football: Refer to Exercise 7.51.

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Question 7.53

Steps 3 through 6 of hypothesis testing for a study of college football: Refer to Exercise 7.51. Remember, the population mean is 16.189, with a standard deviation of 12.128. The results for the four FCS Patriot League games are as follows:

Holy Cross, 27/Bucknell, 10

Lehigh, 23/Colgate, 15

Lafayette, 31/Fordham, 24

Georgetown, 24/Marist, 21

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Putting It All Together

Question 7.54

The Graded Naming Test and sociocultural differences: Researchers often use z tests to compare their samples to known population norms. The Graded Naming Test (GNT) asks respondents to name objects in a set of 30 black-and-white drawings. The test, often used to detect brain damage, starts with easy words like kangaroo and gets progressively more difficult, ending with words like sextant. The GNT population norm for adults in England is 20.4. Roberts (2003) wondered whether a sample of Canadian adults had different scores than adults in England. If they were different, the English norms would not be valid for use in Canada. The mean for 30 Canadian adults was 17.5. For the purposes of this exercise, assume that the standard deviation of the adults in England is 3.2.

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  7. FszSiQp57gD4Uss+V04Nqza8XqbWqIg7hfz1uyAjOXuJ+TxDiM1cNPi0aoJkoFyNYKdXuzb7dYLClra8Nf09rJcyii8UN82IQJkKPZsXO0NzinEZAglwTmj9Vnq0MH0Sw/VC49y0cRg3MqIymqMnW9wCLMYg6S3ltDgBBPqv3TzdP2nelaybidZ8PtC6rfPpx8DdcoehAk24RAXPsDku/rhjrbza10j35KF9kntMsNN5Ay2YzNj0auXCuddLVwIQuSrdPgTOHG9maEmoIZVujw==
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Question 7.55

Patient adherence and orthodontics: A research report (Behenam & Pooya, 2007) begins, “There is probably no other area of health care that requires…cooperation to the extent that orthodontics does,” and explores factors that affected the number of hours per day that Iranian patients wore their orthodontic appliances. The patients in the study reported that they used their appliances, on average, 14.78 hours per day, with a standard deviation of 5.31. We’ll treat this group as the population for the purposes of this example. Let’s say a researcher wanted to study whether a DVD with information about orthodontics led to an increase in the amount of time patients wore their appliances, but decided to use a two-tailed test to be conservative. Let’s say he studied the next 15 patients at his clinic, asked them to watch the DVD, and then found that they wore their appliances, on average, 17 hours per day.

189

  1. 77rka57DxNrKaCw2Tn31QrlpkYiBA4diwtcgPInp5TWc4eown6u6gIwcOs/BbIQ6vgbC9vU+1EU4CHUuEnjoHBMda+VbXL+fR8HdbM7GWDWh+dQR
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Question 7.56

Radiation levels on Japanese farms: Fackler (2012) reported in the New York Times that Japanese farmers have become skeptical of the Japanese government’s assurances that radiation levels were within legal limits in the wake of the 2011 tsunami and radiation disaster at Fukushima. After reports of safe levels in Onami, more than 12 concerned farmers tested their crops and found dangerously high levels of cesium.

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Question 7.57

You have conducted a study with 120 participants (60 female, 60 male) about the relation between attitudes toward cohabitation before marriage (on a 30-item scale) and self-reported sexual behaviors (on a 20-item scale). Most respondents filled out both scales completely. Everyone completed the scale assessing attitudes toward cohabitation, but 1 participant marked the highest possible score on every item on both scales and finished very quickly. In addition, 13 women and 4 men did not complete the 20 questions about sexual behavior. Of these, 9 women and 2 men did not respond at all to the questions about sexual behavior; 3 women and 1 man answered just 10 of these questions; and 2 women and 1 man did not answer just 1 question.

  1. UyWCjdB0SAX0FsHqFjj9vh6KZAIX+0juGukUoZkt94D5IkDf2IqDns+c4bTrE18Fx+1IafCl/o4b0rPI5+bFFtuzXSZzJB3j9aPlfLi2rGWgL0N7ubyGAvoxBkX85c7p
  2. ppOfsZH4cRhfi/WrVE6z0Ij4dCIL6L57k+EAUACkzDsdA30SWR+hv6+s/PlpJL2uq3X+8ZbsUg1rv2+vpR4x23J5Qjpay/CmMkvTWP8lKpwlLQP9U+sc2Qf2OvHm6XY0muDK0Q==
  3. NNQ4ZudvI+JkEzTcczpnTxxfLAZFcJAkndlst3sF2R18P0dC7XwonxtzEM93o5MEh83RjNqgqNIGrnwRhvOJYZ1sRwN0TcWZPAoyHeomcdUfDeqT5RNxqGcKJptn2G75sNXeHzuXh6URL7ssqdS4YGvTADqLwPtQwdUPaE18DloTNC8wJtKIEmgUWjY=
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Question 7.58

You have just conducted a study testing how well two independent variables, daily sugar intake (as assessed by a 25-item eating habits scale) and physical activity (as assessed by a 20-item daily physical activity scale), predicted the dependent variable of blood sugar levels. There were only 17 participants to start with, and 3 of them dropped out before having their blood sugar levels assessed. In addition, 2 participants left one item blank on the physical activity scale, and 4 other participants left most of the data on the eating habits scale blank. At their debriefing interview, they said they just couldn’t estimate food intake with any accuracy.

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  3. uR8yIKEg6R/jyGVjnj7XZYyWM2Qsu14RJv+ei69cgWOPkQ8Etdrw9uAkEm0StDEpSUZzLcGgDOW54nBR6hpyJl0GgpJ+2d39dHrNSmZwbSiCCjZWThub7gOjwn4wy2X5QEJ7Gj4xxAVhbMwEltFTmfwbvoX7C2Zt3iT3pdCFeV3/lW96YAI4Lc+qE8vyS/WWp8D4APBlL7z/o7MM
  4. r5niq2kZND63KBpbrkkg7UUlqOHQTYmMcTtFsoHD1lA36tLSCb8lwyI+lhfg5kvn735U9yJm0/n8xVhBT5KxmtNou3+gRKXy

Question 7.59

In Next Steps, we noted that the z distribution is sometimes used to identify potential outliers in a data set. Box Office Mojo (2013) provides data on U.S. box office receipts for major films. Here are worldwide box office grosses for a randomly selected sample of 15 of the 100 top-grossing films of 2012. Note that we have rounded figures to the nearest million. The figures reported below are millions of dollars.

190

Movie Millions of dollars
Marvel’s The Avengers 1512
Flight 162
Skyfall 1109
Wrath of the Titans 305
Tyler Perry’s Madea’s Witness Protection 66
Zero Dark Thirty 109
Lincoln 275
Moonrise Kingdom 68
Life of Pi 609
The Lucky One 99
The Bourne Legacy 276
The Watch 68
Rock of Ages 59
Cloud Atlas 131
Snow White and the Huntsman 397
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