Suppose an opinion poll on a referendum in 4 city districts yields the following data: Yes No Undecided Total District 3 18 20 12 50 District 8 26 16 8. 50 District 11 20 24 6. 50 District 16 28 12 10 50 Total 92 72 36 200 Let H, be the hypothesis that the voter opinion on the referendum is homogeneous in the 4 districts. (a) Find the ? value. (b) Find the degrees of freedom (df). (c) Test H, at a= 0.10 significance level.
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- The table below summarizes data from a survey of a sample of women. Using a 0.01significance level, and assuming that the sample sizes of 800 men and 300 women are predetermined, test the claim that the proportions of agree/disagree responses are the same for subjects interviewed by men and the subjects interviewed by women. Does it appear that the gender of the interviewer affected the responses of women? Gender of Interviewer Man Woman Women who agree 498 247 Women who disagree 302 53 Compute the test statistic, rounding to three decimal places. Find the critical value(s). (Round to three decimal places) What is the conclusion based on the hypothesis test?A U.S. Food Survey showed that Americans routinely eat beef in their diet. Suppose that in a study of 49 consumers in Illinois and 64 consumers in Texas the following results were obtained from two samples regarding average yearly beef consumption: Illinois Texas = 49 = 64 = 54.1lb = 60.4lb S1 = 7.0 S2 = 8.0 Formulate a hypothesis so that, if the null hypothesis is rejected, we can conclude that the average amount of beef eaten annually by consumers in Illinois is significantly less than that eaten by consumers in Texas.The management of the Seaside Golf Club regularly monitors the golfers on its course for speed of play. Suppose a random sample of golfers was taken in 2005 and another random sample of golfers was selected in 2006. The results of the two samples are as follows: 2005 2006 x1= 225 x2= 219 s1= 20.25 s2= 21.70 n1= 36 n2= 31 Based on the sample results, can the management of the Seaside Golf Course conclude that the average speed of play was different in 2006 than in 2005? Conduct the appropriate hypothesis test at the 0.10 level of significance. Assume that the management of the club is willing to accept the assumption that the populations of playing times for each year are approximately normally distributed.
- 19. A local brewery produces three premium lagers named Half Pint, XXX, and Dark Knight. Of its premium lagers, the brewery bottles 40% Half Pint, 40% XXX, and 20% Dark Knight. In a marketing test of a sample of 80 consumers, 26 preferred the Half Pint lager, 42 preferred the XXX lager, and 12 preferred the Dark Night lager. Using a chi-square goodness-of-fit test, test whether the production of the premium lagers matches these consumer preferences using a .05 level of significance. 19a. Step 2: Compute the df and locate the critical values. df = _______ Critical value = ________19. A local brewery produces three premium lagers named Half Pint, XXX, and Dark Knight. Of its premium lagers, the brewery bottles 40% Half Pint, 40% XXX, and 20% Dark Knight. In a marketing test of a sample of 80 consumers, 26 preferred the Half Pint lager, 42 preferred the XXX lager, and 12 preferred the Dark Night lager. Using a chi-square goodness-of-fit test, test whether the production of the premium lagers matches these consumer preferences using a .05 level of significance. 19. Step 1: Which of the following is the correct set of hypotheses?A. H0: The preferences will not match production (40% Half Pint, 40% XXX, 20% Dark Knight); and H1: The preferences will match production B. H0: \mu_{1}μ1 = \mu_{2}μ2 = \mu_{3}μ3; and H1: At least one of the categories will be different than the others C. H0: The preferences will match production (40% Half Pint, 40% XXX, 20% Dark Knight); and H1: The preferences will not match production 19b. Step 2: Compute the df and locate the…19. A local brewery produces three premium lagers named Half Pint, XXX, and Dark Knight. Of its premium lagers, the brewery bottles 40% Half Pint, 40% XXX, and 20% Dark Knight. In a marketing test of a sample of 80 consumers, 26 preferred the Half Pint lager, 42 preferred the XXX lager, and 12 preferred the Dark Night lager. Using a chi-square goodness-of-fit test, test whether the production of the premium lagers matches these consumer preferences using a .05 level of significance. 19. Step 3: Compute the test statistic -- Chi-square χ2 = (use 2 decimal places) _____________ Step 4: Decision and Conclusions 19. Step 4: Decision: A. Reject H0 B. Retain H0 19. Step 5: Conclusion: Did the production of the premium lagers match consumer preferences? A. Yes. The observed frequencies did not differ from the expected frequencies. B. No. The observed frequencies differed from the expected frequencies.
- 19. A local brewery produces three premium lagers named Half Pint, XXX, and Dark Knight. Of its premium lagers, the brewery bottles 40% Half Pint, 40% XXX, and 20% Dark Knight. In a marketing test of a sample of 80 consumers, 26 preferred the Half Pint lager, 42 preferred the XXX lager, and 12 preferred the Dark Night lager. Using a chi-square goodness-of-fit test, test whether the production of the premium lagers matches these consumer preferences using a .05 level of significance.The owner of a computer company claims that the proportion of defective computer chips produced at plant A is higher than the proportion of defective chips produced by plant B. A quality control specialist takes a random sample of 80 chips from production at plant A and determines that there are 12 defective chips. The specialist then takes a random sample of 90 chips from production at plant B and determines that there are 10 defective chips. Let pA = the true proportion of defective chips from plant A and pB = the true proportion of defective chips from plant B. Which of the following is the correct P-value for the hypotheses, ?The owner of a computer company claims that the proportion of defective computer chips produced at plant A is higher than the proportion of defective chips produced by plant B. A quality control specialist takes a random sample of 80 chips from production at plant A and determines that there are 12 defective chips. The specialist then takes a random sample of 90 chips from production at plant B and determines that there are 10 defective chips. Let pA = the true proportion of defective chips from plant A and pB = the true proportion of defective chips from plant B. Which of the following is the correct standardized test statistic for the hypotheses, ?
- Let p1 and p2 be the respective proportions of women with iron-deficiency anemia in each of two developing countries. A random sample of 1900 women from the first country yielded 513 women with iron-deficiency anemia, and an independently chosen, random sample of 1700 women from the second country yielded 515 women with iron-deficiency anemia. Can we conclude, at the 0.10 level of significance, that the proportion of women with anemia in the first country is less than the proportion of women with anemia in the second country? Perform a one-tailed test. Then complete the parts below.Carry your intermediate computations to three or more decimal places and round your answers as specified in the parts below. a. State the null hypothesis H0 and the alternative hypothesis H1. b. Find the values of the test statistic. c. FInd the p-value. d. Can we conclude that the proportion of women with anemia in the first country is less than the proportion of women with anemia in the second country?In a public opinion survey, 60 out of a sample of 100 high income voters and 40 out of a sample of 75 low income voters supported a decrease in value added tax VAT. Conclude at the 5% level of significance that the proportion of voters favoring a VAT Degrees difference between high and low income voters. (Where P1 is the proportion of all high income voters who is supported a decrease in VAT, p2 is the same for the low income voters ). The value of the test statistic to test the hypothesis is _____ and hence _____ A. T = - 0.668,accept H0 B. T = - 4.117,reject H0 C. Z= 0.882,accept H0 D. T = 2.313,reject H0 E. Z = 0.882,reject H0In the recent census, three percent of the U.S. population reported being two or more races. However, the percent varies tremendously from state to state. Suppose 2 random surveys are conducted. In the first random survey, out of 1,000 north dakotans, 9 people reported being of two or more races. In a second random survey, out of 500 nevadans, 17 people reported being of 2 or more races. Conduct a hypothesis test to determine if the proportions are the same for the two states or if the proportion for Nevada is statistically different than that of north Dakota.