# Chapter 1. Planning Studies Part 1: The Power of a Statistical Test

true
Stat Tutor
true
true

1:09

### Question 1.1

q+8DmJpt4VVc0qJZB6VkgBMPaxonnLToJw2Ur1dd0g6PF/CmbqhUoK2drv+qqE08x2xngAhSX8Lsoajzgl16+H1KbNa0eDzAkQcjKU3uFXqUwvFUnJTpZcjzF2nXZ2vyOgX0cKIm8b1I58iXzWWLAl5H3pk8YCI70YRPsnQAYJXHVeGokRFRhxgoO4qhHTIT
Incorrect. The inability of a test to detect significance due to small sample size is an important issue for tests of significance.
Correct. The inability of a test to detect significance due to small sample size is an important issue for tests of significance.
Incorrect. Try again.
2

2:43

### Question 1.2

Which of the following are subjectively set by the researcher in the planning stage of a study when determining sample size? Select all that apply.

wg8JNehuALfILP6Sa. Level of significance

wg8JNehuALfILP6Sb. Size of the effect for which she would like to detect significance

3hMJDRP6OS+3EJIbc. The sample mean and sample standard deviation

wg8JNehuALfILP6Sd. Power (probability that she would like to have of rejecting an incorrect null hypothesis)

Incorrect. Significance level, effect size and power are all specified by the researcher in order to determine sample size.
Correct. Significance level, effect size and power are all specified by the researcher in order to determine sample size.
Incorrect. Try again.
2

### Question 1.3

HntiGMywWB1FAuMRrLrQAo7lbhnL017kztcQy1lJWyhfN+Jb7EHTr/knoIcXPq7Jcvy62FvXxb/iYnMNYUo0P/oXkuXyMXE45oSt5OKHUwEB1WYQU60PDa/oVpdyo+tyFfYlTNWNXVeSk8k31HHpDI1THKNQnAkx/kwZWL4jY8JYFLDQQsNuQh73+ys752DCFXuCK0Vc5ilh/AKl/1C6S+dFbrETpbPNHWmmOHNhyS6GATOtKunacLOxnX9YUMwCVba8IYdVE16A4Q5yy5QzJI0jDSzHR7ooDkPrOYVMr82GPnDYbaRA4pFpfFSy5Dw2WI69jT0AEWmuvpx3M71z4UxdvvBmJb4RQM/2vB3LUMHbUjuEEXx6o02QOOPCKV2ofVJIpFSh2s/qiU0CBuf3hA==
Incorrect. Power is the probability of doing what we usually want to do when performing a test of significance. We want to reject H0 when it is incorrect. So, power is the probability of rejecting H0 when it is incorrect.
Correct. Power is the probability of doing what we usually want to do when performing a test of significance. We want to reject H0 when it is incorrect. So, power is the probability of rejecting H0 when it is incorrect.
Incorrect. Try again.
2

4:35

### Question 1.4

QYjmG82SWR7T0wyt9YuM7FPh0Oj0VNQlEQaJ/jd1YO9EY6rY2OxO5B0zMwRulx6/mcOC8oAiYiO5J+h/fwx4bxwmgZE1p779Pwbb17Lx3+ExJoOQqctDyvkjL+Ig8P2Vbgq1uaTqNAeRHyYHAa/19jJe6KcyR0VygJ0OqZo30EfBvR8wBqd8Ezax8ZyJ0qyusloVODQj4je8AGGWq7NxFfxV+/qJS00LP+STBbzKnMXWbN5z85kSPwgoIqcAJ2co1zXH7B3FO9+uYqSA4q3iDs6yxlSgxQezivg0u3MRKULtmDgaRwoWiWUOCuIljdRufNPwtPv5rVJCCOHUFSAx38H3Z070BTgvRIIRisobrxYcpZZWOXROsLAvE1IMqzcH0M5EsL1YSR6DdhLIoDufSdmZ3SvcS26QNbySS5YWL3xMiVm8gvSP8n1EwYGyA5BCj548vbE0e88=
Incorrect. Effect size is the size of the difference between μ0 = 483 and the value of μ for which the researcher wishes to detect significance. District officials want to detect signficance for a value of μ = 503 or higher. So, effect size = 20 = 503 – 483.
Correct. Effect size is the size of the difference between μ0 = 483 and the value of μ for which the researcher wishes to detect significance. District officials want to detect signficance for a value of μ = 503 or higher. So, effect size = 20 = 503 – 483.
Incorrect. Try again.
2

### Question 1.5

sT3AtFhCpJkIjJ5/pGF/ONRe7D/L8A4tL5wXQ93sHCKaZizOPuYp+2O92pkGdRDxdyYGfNQLdqCn36OntS0kuV8M2KXHtm7DfkIoRVs8B36jPXRqIudBKhkWL07AQdyBIQ530M1qbStHc7MK8pM8nDndzvcC9eURIm+NsxaKKyD2GRZvH9yp5iFwqaI=
Incorrect. For this example, district officials wanted to be 90% confident in rejecting H0 when the true mean was 503 or higher.
Correct. For this example, district officials wanted to be 90% confident in rejecting H0 when the true mean was 503 or higher.
Incorrect. Try again.
2

5:15

### Question 1.6

MPc6zBkNxHkkLCLa65AniSvR6T8P4Z3DdAYFzKl1UnDeoMe488I1U6u07tzEkRLXaUJVRN+FBDiTeIVG4wtR+lW3I6WJxTCb1X2oOlkM6PkYOTu3gIVzqWTtFUt8PPSXtAc49yRE/6qUmIpyqE87Z8zhopu36KvcPz44nm4ScYqj11iB0R5RIm+ruYQ=
Incorrect. The formula for finding sample size for a test of significance is complicated, so researchers use statistical software to determine sample size.
Correct. The formula for finding sample size for a test of significance is complicated, so researchers use statistical software to determine sample size.
Incorrect. Try again.
2

5:57

### Question 1.7

UWFNHT7KrZnqj/hJ0FBbgmPdstbTVL2MUsepDAFqlB6/EOgrTJ1yGMkMA9gsv5acjGZZme0QSWBiSghSI5ipL4Dsyk2v5HFUg26u4aovK04oOS8QXMHS5aXmoBJsNEuocNmPilZqdQcqVI65yIfKi9nWigYlgWiHUi1Zz4MYE9jRG3ji
Incorrect. The formula for finding power for a test of significance is complicated, so researchers use statistical software to determine power.
Correct. The formula for finding power for a test of significance is complicated, so researchers use statistical software to determine power.
Incorrect. Try again.
2

8:22

### Question 1.8

1ciGCjh15VUfhvXRIUv57gnCgQFcTSOwiPsIsMib8DoJdgHOwlGJi2O3h2ndsGj5AsHs7loguwtsD+lLRoO1UATfyVtaKSX+JpNdxIZ6x04vEfieTph6pxpCIEWSNySot7eNcaEB5fFBdeWZ428duXzFKiws7qIOfDCixqOilkrJnN6lIlSrZNmS5LRjEux/p+Q1KWe0H8r+OKch+wzIeDaN39WWCaUxfxsQhMS96YI=
Incorrect. Since α is the probability of rejecting H0 when it is correct and power is the probability of rejecting H0 when it is incorrect, both are probabilities of “rejecting H0," just on different curves. So, both are on the same side of the line in the “reject H0” regions of their respective curves.
Correct. Since α is the probability of rejecting H0 when it is correct and power is the probability of rejecting H0 when it is incorrect, both are probabilities of “rejecting H0," just on different curves. So, both are on the same side of the line in the “reject H0” regions of their respective curves.
Incorrect. Try again.
2

### Question 1.9

Incorrect. α and β (probability of a type II error) are on opposite sides of the line and on different curves.
Correct. α and β (probability of a type II error) are on opposite sides of the line and on different curves.
Incorrect. Try again.
2

9:52

### Question 1.10

IXJW3qVbTp5X3MYfRYUC/IQYLgRQXJRU0m9IaTlaopyOMEJ4DluS7wbARJY+h0/uxwQvyVF/up8Ra/pGYiAHPWwGcbRNCUY8En/m3+w5axlNOBcpsZ0TPSJl4VX1ARe7tYYqMK/bMA/x+OpRkrBnegIzygr+8knwTw6Pnw==
Incorrect. Decreasing α from 0.10 to 0.05 moved the line to the right. This decreased the area representing power on the sampling distribution of $$\overline{x}$$ curve with center at μ = 28.
Correct. Decreasing α from 0.10 to 0.05 moved the line to the right. This decreased the area representing power on the sampling distribution of $$\overline{x}$$ curve with center at μ = 28.
Incorrect. Try again.
2

10:10

10:11

### Question 1.11

6K9UlB3uWYVhOjfYDFyquG29Di/WWXef6qfl7Jw5WO6UVR38ryRmTHFbCksVVGTkOLKDDuQglqZvLwIg6YpGqvE30wBpNlgiHEyUbASVC2oaPlTpv38/h2oFf7GdD9+cqoVPvA==
Incorrect. Increasing α moves the line to the left. This increases the area representing power on the sampling distribution of $$\overline{x}$$ curve with center at μ = 28.
Correct. Increasing α moves the line to the left. This increases the area representing power on the sampling distribution of $$\overline{x}$$ curve with center at μ = 28.
Incorrect. Try again.
2

10:21

### Question 1.12

nwKSYWAq8xHMEY78XblR2yKznls60zDT5wsSMA7WOhdl82QNsanCxGl+Azl4hk0tMfurZZyrVToQ4nOP2oaypI8tJkeHP6rkmBNF0Ul1rfbwPZYcVBtt6Q==
Incorrect. Increasing α increases power, so power is higher for bigger α.
Correct. Increasing α increases power, so power is higher for bigger α.
Incorrect. Try again.
2

11:42

### Question 1.13

Incorrect. The power in this example is only slightly over 0.5, maybe about 0.6. This is too low to be reasonable, so it should be increased.
Correct. The power in this example is only slightly over 0.5, maybe about 0.6. This is too low to be reasonable, so it should be increased.
Incorrect. Try again.
2

12:10

### Question 1.14

R95NzO9kvtAs3RIBRcVN/29UwtKSaBoI1lmwPhCDRbAEX7a+xRqjRW1axgt+nsIAJf1aodGmjr5ucEJXacwQNJbQ4GbVnBdSzcZOZSv0SBRE/ii4DBlr7zzzNq9bxhYH4FYymPlI3ydfIOiOF6vnEXFoZUpGfx3IK7CMDtH1iafNokoZdFTUztRU04dnztbK7yGeKBf8GV0NWQHu6NtHgzO9jQftNIRP9GOxEWdEf7t2I1Q7DeupRcQWPJqfgoUjKy71tfd05IDtuDc0WMxN+L5BC+e+RFF6Jf4Zmih1DnvFbMiGwE2AwwsvuJp95TjO3jDpqQ==
Incorrect. Increasing sample size, decreases the standard deviation of the sampling distribution of $$\overline{x}$$, making both curves taller and skinnier. Since α is set at 0.10 and it determines the location of the line, power is increased.
Correct. Increasing sample size, decreases the standard deviation of the sampling distribution of $$\overline{x}$$, making both curves taller and skinnier. Since α is set at 0.10 and it determines the location of the line, power is increased.
Incorrect. Try again.
2

12:43

### Question 1.15

ueKRS2K0n9Rem9jrF6hDt55IHtgLSF2kgXgoZnUBep6kCuA0nEPiTu/3yNdi7ChleUSgmml2K/VklU/Ei/rUDgu7bYNI1R4HhUH4Vc5htlTdifmVhGJdbwECCGim1Unwla2JTQZVaJXXBwjMDA2k5g==
Incorrect. Increasing sample size increases power, making detection of significance better.
Correct. Increasing sample size increases power, making detection of significance better.
Incorrect. Try again.
2

14:28

### Question 1.16

gAsgln89ZYSJkstGyP1B+TbFRm3Rov6S0oWhM/4vCcc2EnrvIZ0xioeTklveK1b5kx9b4SmCv37CrCJ/vHR3UDz+Arjt2Un73B5I3b2bC5RlwGYH4rfiwKVFmIpqtIO7ZtDS+o52FaYsowQVfJG4HWiQfY3600AV
Incorrect. We need to know the effect size in order to determine power. Effect size equals the difference between the true value of µ and the hypothesized value of µ, so power depends on both values for µ.
Correct. We need to know the effect size in order to determine power. Effect size equals the difference between the true value of µ and the hypothesized value of µ, so power depends on both values for µ.
Incorrect. Try again.
2

16:47

### Question 1.17

7/iFzeHeBDlbWqS0WmYRTDed6FNpDFdZ1Mtfl2IidIleooymgNlop/gCSKuQs/GN8omETLA+GeESz1VXrpZ+rRtdp5KtiGV5DYIRayqp76EvpZko
Incorrect. The smaller the effect size, the smaller power is; the larger the effect size, the large power is.
Correct. The smaller the effect size, the smaller power is; the larger the effect size, the large power is.
Incorrect. Try again.
2

17:47

17:47

### Question 1.18

BamgBckeyzW9gJia2t7Lg+xAYFK5ocf94YSrlsz+f6BzKHzW//7wDlEtGX2YE1lOtuQEL3KtN0NFhU+XWWuNMo1ybi/uok/7B0xUuDM7xW/X9XRn2Gz8flpvYiRXvTGfJg2ROarO1Ap37q60ewx59LN93fQdEyl80UeT2BG7LgOWwlzXOqAja5sL7x4=
Incorrect. The larger the effect size, the larger power is. Effect size equals the difference between the true value of µ and the hypothesized value of µ.
Correct. The larger the effect size, the larger power is. Effect size equals the difference between the true value of µ and the hypothesized value of µ.
Incorrect. Try again.
2

19:15

### Question 1.19

qgkRbRWf5A18jgSq8qAv/jDo3Z79b6VpECrNkhV6yGMqF3xkQSAWGlBlwSWmi6Wbu44aTrgnnh5JXLt95gzt1J2pZ2UJWe3+Q4SIrsRfMznHmBdcwVKG4GoRExGa/G6nhry74yewwjtvH2ewNufRjjIPyimPxl1K
Incorrect. Detecting a “small” effect size requires a larger sample size than detecting a large effect size.
Correct. Detecting a “small” effect size requires a larger sample size than detecting a large effect size.
Incorrect. Try again.
2

19:59

### Question 1.20

Which of the following increases power? Select all that apply.

wg8JNehuALfILP6Sa. Increasing α

3hMJDRP6OS+3EJIbb. Decreasing α

wg8JNehuALfILP6Sc. Increasing sample size

3hMJDRP6OS+3EJIbd. Decreasing sample size

Incorrect. Increasing either α or sample size increases power.
Correct. Increasing either α or sample size increases power.
Incorrect. Try again.
2