Please explain all steps who we get the answers. Thanks! 5. A manufact urer rece
ID: 3046872 • Letter: P
Question
Please explain all steps who we get the answers. Thanks!
5. A manufact urer receives parts from two suppliers. A simple random sample of 400 parts from Supplier 1 finds 20 defective. A simple random sample of 200 parts from Suppi 2 finds 20 defective. Let pi and p be the proportion of all parts from Suppl plier 1 and Supplier 2, respectively, that are defective. What is the relative risk that a part from Supplier 1 is defective as compared to a part from Supplier 2? RR=0.05 RR = 0.15 A) B) C) RR 0.5 D) RR-2 6. There is substantial interest in the health benefits of the consumption of high amounts of fiber in diets. A market research team is interested in the public acceptance of a new high-fiber cereal (more than 8 grams of fiber per serving) that is to be marketed. To that end, the researchers selected a random sample of subjects from one region of the country. The selected subjects were provided with two bowls of cereal. One bowl contained the new cereal and the other bowl contained a well-known cereal. The bowls were presented in random order and subjects were asked which cereal they preferred. The study was repeated independently in a second region. In the first region, of the 400 subjects, 220 preferred the new cereal; in the second region, 195 of the 300 subjects indicated a preference for the new cereal. The researchers wanted to test whether the proportions of consumers who preferred the new high-fiber cereal are the same or different in the two regions. What null and alternative hypotheses should they establish? A) Ho: p1=p2 against His pPP2 B) Ho: pi-p 2 against Ha: p1# p2 C) Ho: P-P against Ha: Pp D) Ho: p- p against H: p> E) Ho: pl-p2=0 against Ha: p1-p2=0.5 7. A company is being criticized for having female employees as a vast minority. The company claims that 40% of their employees are women. You wish to test the hypotheses that the proportion of women at this company is indeed equal to what the company claims. You will test the hypotheses H: p-0.40 versus H. 040, where p is the proportion of female employees at this company. A simple random sample of 16 employees of this company is taken and only three of them are female. What is a 90% plus four confidence interval for p?
Explanation / Answer
Solution:-
6) (C)
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: P1 = P2
Alternative hypothesis: P1 P2
Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the proportion from population 1 is too big or if it is too small.
Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method is a two-proportion z-test.
Analyze sample data. Using sample data, we calculate the pooled sample proportion (p) and the standard error (SE). Using those measures, we compute the z-score test statistic (z).
p = (p1 * n1 + p2 * n2) / (n1 + n2)
p = 0.5929
SE = sqrt{ p * ( 1 - p ) * [ (1/n1) + (1/n2) ] }
SE = 0.03753
z = (p1 - p2) / SE
z = - 2.66
where p1 is the sample proportion in sample 1, where p2 is the sample proportion in sample 2, n1 is the size of sample 1, and n2 is the size of sample 2.
Since we have a two-tailed test, the P-value is the probability that the z-score is less than -2.66 or greater than 2.66.
Thus, the P-value = 0.0078
Interpret results. Since the P-value (0.0078) is less than the significance level (0.05), we have to reject the null hypothesis.