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e Statistics ALL answers need to be recorded into the Canvas "Quiz" for grading; Each Q should be worked on your own paper; See Canvas for exact due date; Your hand-written solutions need to be uploaded into the module assignment to substantiate (as a pdf file); Proportions Two-Sample CIs and HTs Goodness-of-Fit (GOF) Notes: Some of the HT Qs utilize the alternate notation of using words instead of (population) numbers MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. 1) A polling agency wants to estimate the proportion of U.S. citizens who support the president's 1) domestic policies. They surveyed 2500 U.S. citizens and found a 95% confidence interval for the difference in proportions between men and women who support the president's domestic policies as (-0.025 to 0.050) where population 1 is men and population 2 is women. Select the correct interpretation of this result. })"The interval does not contain zero which shows that there is no significant difference in the proportions between men and women. he interval contains zero which shows that there is no significant difference in the proportions between men and women. C) The interval contains zero which shows that men are more likely than women to disagree with the president's foreign policies. D) The interval contains zero which shows that women are more likely than men to disagree with the president's foreign policies. 2) A researcher believes that the proportion of women who exercise with a friend is greater than the 2) proportion of men who exercise with a friend. He takes a random sample from each population and records the response to the question, "Have you exercised with a friend at least once in the last seven days?" The null hypothesis is Hp: pwomen = Pmen. Choose the correct alternative hypothesis. Ha: Pwomen > Pmen /B(Hai p=0 C) Ha: pwomen #Pmen JHa: Pwomen < Pmen Ha® 4>

3) A researcher asks random samples of residents of two separate counties as to whether they had 3) B purchased organically grown food in the last three months. He wanls to determine whether the proportion of residents of one county who purchase organically grown food is greater than the proportion of residents of the second county who purchase organically grown food. Choose the appropriate test and name the population(s). Hee 0> fa One-proportion z-test: the population is all residents of a state. Two-proportion z-test; one population is all residents of the first county and the other population is residents of the second county. C) Two-proportion z-test; one population is all adults who buy organically grown food and the other population is all adults who do not buy organically grown food. /Bf One-proportion z-test; the population is all residents of the first county. 4) A researcher believes that the reading habits of men and women are different. He takes a random 4) L sample from each population and records the response to the question, "Did you read at least one book last month?" The null hypothesis is Ho: Pwomen = Pmen. Choose the correct alternative hypothesis. Ha: Pwomen > Pmen Ha: Pwomen < Pmen a: Pwomen *Pmen /BfHai p=0 5) A researcher believes that the proportion of children who attend elementary school ina rural 5 D setting are more physically active than the proportion of children who attend elementary school in an urban setting. The researcher collects a random sample from each population and records the proportion of children in each sample who reported participating in at least one hour of rigorous activity a day. The data is summarized in the table below. Assume the all conditions for proceeding with a two-sample test have been met. Rural Urban n =90 n, =78 x =74 x, =55 we 2-statistic and p-value for this hypothesis test. Use a 5% significance level. z=-1.79, p = 0.037. There is insufficient evidence to reject the null hypothesis. _ABY7 =071, p = 0.073. There is sufficient evidence to reject the null hypothesis. /é: 7 =0.82, p = 0.073. There is not sufficient evidence to reject the null hypothesis. =1.79, p = 0.037. There is sufficient evidence to reject the null hypothesis. %r L.q f’: 2,037

6) A researcher believes that children who attend elementary school in a rural setting have lower 6) A obesity rates then children who attend elementary school in an urban setting. The researcher collects a random sample from each population and records the proportion of children in each sample who are clinically obese. The data is summarized in the table below. Assume that all conditions for proceeding with a two-sample test have been met. Rural Urban 0.< ()i n =95 n, =100 x=14 | x=26 £ =185 £ 0.025F < TR .. Find the z-statistic and p-value for this hypothesis test. Use a 5% significance level. 7 = -1.95, p = 0.026. There is not sufficient evidence to reject the null hypothesis. /B)'z =1.95, p = 0.026. There is sufficient evidence to prove that the population proportions are the same, €)'z =-1.85, p = 0.032. There is not sufficient evidence to reject the null hypothesis. D) z = -1.95, p = 0.026. There is sufficient evidence to reject the null hypothesis. I 7) Read the following then choose the appropriate test and name the population(s). A researcher asks a random sample of 200 men whether they had made an online purchase in the last three months. He wants to determine whether the proportion of men who make online purchases is less than 0.18. A) Two-proportion z-test; the population is the 200 men surveyed. fi‘ One-proportion z-test; the population is all men. C) One-proportion z-test: the population is all adults who make online purchases. D) Two-proportion z-test; one population is all men who make online purchases and the other population is all men who do not make online purchases. Construct the indicated confidence interval for the difference between population proportions py - p2. Assume that the samples are independent and that they have been randomly selected. 8) Inarandom sample of 300 women, 45% favored stricter gun control legislation. In a random 8) A sample of 200 men, 25% favored stricter gun control legislation. Construct a 98% confidence interval for the difference between the population proportions p1 - p2. 0.102 < p1 - p2 <0.298 B) 0.114 < p1 - pp < 0.286 C) 0.092 < p7 - p2 < 0.308 D) 0.118 < pq - pp < 0.282 9) In arandom sample of 500 people aged 20-24, 22% were smokers. In a random sample of 450 9) c people aged 25-29, 14% were smokers. Construct a 95% confidence interval for the difference between the population proportions p1 - p2. A) 0.035 < p1-p2<0.125 B) 0.025 < p1 - p2 < 0.135 (O0032<p1-p<0128 D) 0.048 < p1 - pp < 0.112 Provide an appropriate response. 10) A chi-square goodness-of-fit test is to be performed. The relative frequencies for the null 10 3 hypothesis and the sample size are given. True or false, the assumptions for using a chi-square goodness-of-fit test are satisfied? Sample size: n = 100 Relative frequencies: 0.31, 0.19, 0.12, 0.2, 0.18 A) True @ False 3 I — S S S e T S

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