a. Use the data given to test the following hypotheses. (Round your answer to 2 decimal places, eg. 15.25) The value of the test statistic is and we b. Use the p-value to reach a statistical conclusion. (Round your answer to 4 decimal places, e.g. 0.1254)
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- Q1. An anthropologist wants to collect data to determine whether the two different cultural groups that occupy an isolated Pacific Island grow to be different heights. The results of his samples of the heights of adult females are as follows Do these samples constitute enough evidence to reject the null hypothesis that the heights of the two groups the same? Set alpha to 0.05 1.What are the appropriate null and alternative hypothesis? 2. What is the Test statistics? 3.What is the value of the test statistic? 4. For a significance level of 0.05, what is the critical value? 5.What is the appropriate decision and conclusion?Step 1 of 3 : State the null and alternative hypotheses for the test. Fill in the blank below. H0: μd=0 Ha: μd⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯0 Step 2: What is the test statistic? Step 3: Do we reject the null hypothesis? Is there sufficient or insufficient data?The recommended daily dietary allowance for zinc among males older than age 50 years is 15 mg/day. An article reports the following summary data on intake for a sample of males age 65−74 years: n = 116, x = 12.5, and s = 6.35. Does this data indicate that average daily zinc intake in the population of all males age 65−74 falls below the recommended allowance? (Use ? = 0.05.)State the appropriate null and alternative hypotheses. H0: ? = 15Ha: ? ≠ 15H0: ? = 15Ha: ? > 15 H0: ? = 15Ha: ? ≤ 15H0: ? = 15Ha: ? < 15 Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) z = P-value = State the conclusion in the problem context. Do not reject the null hypothesis. There is not sufficient evidence that average daily zinc intake falls below 15 mg/day.Reject the null hypothesis. There is not sufficient evidence that average daily zinc intake falls below 15 mg/day. Do not reject…
- ANSWER THE FOLLOWING PROBLEMS SHOWING COMPLETE SOLUTION ENCLOSE FINAL ANSWER THANK YOU! topic TESTS OF HYPOTHESES FOR A SINGLE SAMPLE Exercise 10.6 The proportion of adults living in a small townwho are college graduates is estimated to be p = 0.6.To test this hypothesis, a random sample of 15 adultsis selected. If the number of college graduates in thesample is anywhere from 6 to 12, we shall not rejectthe null hypothesis that p = 0.6; otherwise, we shallconclude that p= 0.6. (a) Evaluate α assuming that p = 0.6. Use the bino-mial distribution. (b) Evaluate β for the alternatives p = 0.5 and p = 0.7.(c) Is this a good test procedure? Exercise 10.7 Repeat Exercise 10.6 but assume that 200 adultsare selected and the fail-to-reject region is defined tobe 110 ≤ x ≤ 130, where x is the number of college graduates in our sample. Use the normal approxima-tion. ANSWER EXERCISE 10.7 ONLYANSWER THE FOLLOWING PROBLEMS SHOWING COMPLETE SOLUTION ENCLOSE FINAL ANSWER THANK YOU! topic TESTS OF HYPOTHESES FOR A SINGLE SAMPLE Exercise 10.6 The proportion of adults living in a small townwho are college graduates is estimated to be p = 0.6.To test this hypothesis, a random sample of 15 adultsis selected. If the number of college graduates in thesample is anywhere from 6 to 12, we shall not rejectthe null hypothesis that p = 0.6; otherwise, we shallconclude that p= 0.6. (a) Evaluate α assuming that p = 0.6. Use the bino-mial distribution. (b) Evaluate β for the alternatives p = 0.5 and p = 0.7.(c) Is this a good test procedure?The recommended daily dietary allowance for zinc among males older than age 50 years is 15 mg/day. An article reports the following summary data on intake for a sample of males age 65−74 years: n = 111, x = 12.4, and s = 6.69. Does this data indicate that average daily zinc intake in the population of all males age 65−74 falls below the recommended allowance? (Use ? = 0.05.)State the appropriate null and alternative hypotheses. H0: ? = 15Ha: ? > 15H0: ? = 15Ha: ? < 15 H0: ? = 15Ha: ? ≤ 15H0: ? = 15Ha: ? ≠ 15 Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) z = P-value = State the conclusion in the problem context. Do not reject the null hypothesis. There is sufficient evidence that average daily zinc intake falls below 15 mg/day.Reject the null hypothesis. There is sufficient evidence that average daily zinc intake falls below 15 mg/day. Do not reject the null…
- 51% of students entering four-year colleges receive a degree within six years. Is this percent smaller than for students who play intramural sports? 140 of the 297 students who played intramural sports received a degree within six years. What can be concluded at the level of significance of αα = 0.01? The null and alternative hypotheses would be: Ho: ? p μ Select an answer < > ≠ = (please enter a decimal) H1: ? μ p Select an answer > = < ≠ (Please enter a decimal) The test statistic ? t z = (please show your answer to 3 decimal places.) The p-value = (Please show your answer to 4 decimal places.)A question of medical interest is whether jogging leads to a reduction in systolic blood pressure. To learn about this question, eight non-jogging volunteers have agreed to begin a 1-month jogging program. At the end of the month, their blood pressures were determined and compared with earlier values. The data are presented in the Table 1. a. The appropriate hypotheses are: H0 :μ1−μ2 =0 versus Ha :μ1−μ2 /= (does not equal) 0 H0 :μ1−μ2 =0 versus Ha :μ1−μ2 <0 H0 :μ1−μ2 =0 versus Ha :μ1−μ2 >0 b. The value of test statistic is 1. 0.577 2. −0.577 3. 0.237 4. -0.237 c. The p−value of test is 1. 0.816 2. 0.408 3. 0.582 4. 0.291 d. At the significance level calculated in part (c), we conclude that jogging i. Leads to reduction in systolic blood pressureii. Does not lead to reduction in systolic blood pressure54% of students entering four-year colleges receive a degree within six years. Is this percent smaller than for students who play intramural sports? 104 of the 225 students who played intramural sports received a degree within six years. What can be concluded at the level of significance of α= 0.10? b. The null and alternative hypotheses would be: H0= please enter a decimal H1= please enter a decimal c. The test statistic = ? (please show your answer to 3 decimal places.) d. The p-value = (Please show your answer to 4 decimal places.)
- A researcher first decided to conduct a two-tailed hypothesis test, with alpha = .05, but then decided she wants to reduce the risk of a Type I error. What should she do? a. Calculate her statistics more carefully. b. Decrease alpha to .01 c. Increase alpha to .15 e. Conduct a three-tailed testIn doing a hypothesis test of the population proportion at α=0.02 level of significance, we got the p-value to be 0.006. What would our conclusion to the test be? Why? A. Do NOT Reject H0 since the p-value > α B. Reject H1 since the p-value < α C. Reject H0 since the p-value < α D. Do NOT Reject H0 since the p-value < αWe ask a random sample of 1000 New Zealanders their opinion on whether New Zealand should become a republic with a president replacing the Queen as head of state and 350 answer ‘yes’. We are testing the following pair of hypotheses for the value of p, the true proportion of New Zealanders who think that New Zealand should become a republic with a president replacing the Queen as head of state: H0: p = 0.40 Ha: p > 0.40 Select the correct value (to 3 decimal places) of the z-test statistic for this sample from the list below. Select one: a.3.315 b.-3.227 c.-3.315 d.3.227