CHECK THE BASICS

For Exercise 23.1, see page 554; for Exercise 23.2, see page 557.

Question 23.3

23.3 Finding statistical significance. If we conduct 100 hypothesis tests at the 5% level, how many of them would we expect to be statistically significant even if none of them were?

  1. (a) 0

  2. (b) 5

  3. (c) 95

  4. (d) 100

Question 23.4

23.4 Width of a confidence interval. Suppose that the length of a confidence interval is 0.06 when the sample size is 400. To decrease the length of the confidence interval to 0.03, we should take a sample of size

  1. (a) 100.

  2. (b) 200.

  3. (c) 800.

  4. (d) 1600.

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Question 23.5

23.5 Practically significant? A new blend of gasoline costs $1.00 more per gallon than regular gasoline. Tests have shown that gas mileage with the new blend is statistically significantly higher than it is with regular gasoline. The P-value was 0.004. A report about these results goes on to say that the new blend of gasoline increases gas mileage by 2 miles per gallon. Are these results practically significant?

  1. (a) No, because the P-value is small.

  2. (b) No, because a 2 mile-per-gallon increase is probably too small to justify an additional $1.00 per gallon.

  3. (c) Yes, because the P-value is small.

  4. (d) Yes, because a 2 mile-per-gallon increase is bigger than 0.

Question 23.6

23.6 Practically significant? Brook conducted a study for a clothing company to determine if a rewards program caused customers to spend more. Brook found statistically significant results, with a P-value of 0.012. The average amount spent per order before the rewards program was $100, while the average amount spent per order after the rewards program was $223. Are these results practically significant?

  1. (a) No, because the P-value is small.

  2. (b) No, because an average increase of $123 per order is probably too small.

  3. (c) Yes, because the P-value is small.

  4. (d) Yes, because an average increase of $123 per order is more than twice the average amount spent per order before the rewards program.

Question 23.7

23.7 Sacred significance level. A researcher decided prior to conducting research to use a 1% level of significance. The researcher finds a P-value of 0.027. Is it okay for the researcher to change the significance level to 5% to have statistically significant results?

  1. (a) No, because the significance level is set beforehand and should not be changed after the P-value has been calculated.

  2. (b) No, because the researcher should redo the study with a larger sample size to make sure to get significant results.

  3. (c) Yes, because it is okay to change the significance level after the P-value is calculated.

  4. (d) Yes, because the researcher should have chosen the 5% level in the first place.