Owners of a chain of ice cream shops recently examined sales figures and noticed that on a randomly selected day, 21 of 103 ice cream customers form their shop located in the eastern part of the state ordered soft serve ice cream, while 29 of 132 ice cream customers from their shop located in the western part of the state ordered soft serve ice cream. 1) Construct a 95% confidence interval to find the difference in proportions of customers who favor soft serve ice cream in the two parts of the state. B) A) C) D) E)

Owners of a chain of ice cream shops recently examined sales figures and noticed that on a randomly selected day, 21 of 103 ice cream customers form their shop located in the eastern part of the state ordered soft serve ice cream, while 29 of 132 ice cream customers from their shop located in the western part of the state ordered soft serve ice cream. 2) Is there a significant difference in the proportions of customers who favor soft serve ice cream in the eastern and western parts of the state? A) There is a significant difference at the 0.001 level. B) There is a significant difference at the 0.10 level but not at the 0.05 level. C) There is a significant difference at the 0.05 level but not at the 0.01 level. D) There is a significant difference at the 0.01 level but not at the 0.001 level. E) There is no significant difference at the 0.10 level.

The pooled sample proportion for this hypothesis test is 3) A test of hypothesis is used to compare two population proportions. Sample data drawn from each of the two populations is shown below where n is the sample size and x is the number of successes. n1=748 n2= 614 x1= 220 x2= 192 The pooled sample proportion for this hypothesis test is A) 0.2941 C) 0.3127 D) 0.4575 E) 0.6068 B) 0.3025

4) A poll reported that 41 of 100 men surveyed were in favor of increased security at airports, while 35 of 140 women were in favor of increased security. (H0: p1=p2 and Ha: p1p2) What is an appropriate conclusion? A) P-value = 0.0512; There is about a 5.12% chance that the two proportions are equal. B) P-value = 0.4211; If there is no difference in the proportions, there is a 42.11% chance of seeing the exact observed difference by natural sampling variation. C) P-value = 0.0512; If there is no difference in the proportions, there is about a 5.12% chance of seeing the observed difference or larger by natural sampling variation. D) P-value = 0.0086; There is about a 0.86% chance that the two proportions are equal. E) P-value = 0.0086; If there is no difference in the proportions, there is about a 0.86% chance of seeing the observed difference or larger by natural sampling variation.

5) A weight loss center provided a loss for 72% of its participants 5) A weight loss center provided a loss for 72% of its participants. The center's leader decides to test a new weight loss strategy on a random sample size of 140 and found 109 participants lost weight. Should the center continue its new strategy? Test an appropriate hypothesis using α = 0.02 and state your conclusion. A) z = -1.54; P-value = 0.0618. The change is statistically significant. A 90% confidence interval is (71.6%, 84.1%). This is clearly higher than 72%. The chance of observing 109 or more participants of 140 is only 5.71% if the weight loss is really 72%. B) z = 1.54; P-value = 0.0618. The center should not continue with the new strategy. There is a 6.18% chance of having 109 or more of 140 participants in a random sample weigh less if in fact 72% do. The P-value of 0.0618 is greater than the alpha level of 0.02. C) z = 1.54; P-value = 0.9382. The change is statistically significant. A 98% confidence interval is (69.0%, 86.7%). This is clearly higher than 72%. The chance of observing 109 or more participants of 140 is only 94.29% if the weight loss is really 72%. D) z = 1.54; P-value = 0.1236. The change is statistically significant. A 95% confidence interval is (70.4%, 85.3%). This is clearly lower than 72%. The chance of observing 109 or more participants of 140 is only 11.42% if the weight loss is really 72%. E) z = -1.54; P-value = 0.9382. The center should continue with the new strategy. There is a 94.29% chance of having 109 or more of 140 participants in a random sample weigh less if in fact 72% do.

6) An entomologist writes an article in a scientific journal which claims that fewer than 12% of male fireflies are unable to produce light due to a genetic mutation. Identify the Type I error in this context. A) The error of rejecting the claim that the true proportion is at least 12% when it really is at least 12%. B) The error of accepting the claim that the true proportion is at least 12% when it really is at least 12% C) The error of rejecting the claim that the true proportion is less than 12% when it really is less than 12%. D) The error of failing to accept the claim that the true proportion is at least 12% when it is actually less than 12%. E) The error of failing to reject the claim that the true proportion is at least 12% when it is actually less than 12%.

7) A survey investigates whether the proportion of 8% for employees who commute by car to work is higher than it was five years ago. Identify the Type II error in this context. A) The survey concludes that commuting by car is on the rise, but in fact there is no change in commuting. B) The product of the survey's sample size and sample proportion was less than 10. C) The survey concludes that commuting by car is on the rise since the commuting can only increase. D) The survey sampled only a dozen employee commuters. E) The survey states there in no change in commuting, but in fact commuting by car is increasing.

8) At one vehicle inspection station, 13 of 52 trucks and 11 of 88 cars failed the emissions test. Assuming these vehicles were representative of the cars and trucks in that area, what is the standard error of the difference in the percentages of all cars and trucks that are not in compliance with air quality regulations? 0.032 B) 0.025 C) 0.049 D) 0.095 E) 0.070

The painful wrist condition called carpal tunnel syndrome can be treated with surgery or less invasive wrist splints. In September 2002, Time magazine reported on a study of 176 patients. Among the half that had surgery , 80% showed improvement after three months, but only 54% of those who used the wrist splints improved. Is there a significant difference in the percent of patients the showed improvement between the two types of treatments? 9) State the appropriate hypotheses. Ho: pS= p WS Ha: pS≠ p WS 10) Write the formula you would use.

MC Review Chapters 21 and 22 B 2) E 3) B 4) E 5) B 6) A 7) E 8) E