An automobile manufacturer substitutes a different engine in cars that were known to have an average miles-per-gallon rating of 31.5 on the highway with SD=6.6. The manufacturer wants to examine whether the new engine changes the miles-per-gallon rating of the auto-mobile model. A random sample of 100 trial runs gives on average of 29.8 miles per gallon. Is the average miles-per-gallon rating on the highway for cars using the new engine different from the rating for cars using the old engine? Make your conclusion based on a) Critical value at 5% level of significance. b) 95% CI for the mean of miles-per-gallon. c) P-value

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 = 113, x = 12.4, and s = 6.63. Does this data indicate that average daily zinc intake in the population of all males age 65-74 falls below the recommended allowance? (Use a = 0.05.) State the appropriate null and alternative hypotheses. O Ho: H = 15 H: u > 15 O Ho: H = 15 H: u < 15 Ο H: μ15 H:us 15 Ο Η: μ- 15 H: u = 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. O Reject the null hypothesis. There is sufficient evidence that average daily zinc intake falls below 15 mg/day. O Do not reject the null hypothesis. There is sufficient evidence that average daily zinc intake falls below 15 mg/day. O Do not reject the null hypothesis. There…

Find the critical value for a test for correlation with α = 0.01 for a sample size of 18.

A paint company has large outlet stores in two cities. Ten samples of the weekly sales (in tons) for the two cities are as follows. City A: n = 10, X10 = 148.5, S1 = = 4.3. City B: n = 10, Y 10 = 144.2, S2 = 3.8. At a = 0.05 level of significance, test if the weekly sales are different. The following ¨answers" have been proposed. (a) The null hypothesis is that the weekly sales are the same and the alternative is that the they are not the same. By using an F test, we reject the null hypothesis. (b) The null hypothesis is that the weekly sales are the same and the alternative is that the they are not the same. By using an F test, we do not reject the null hypothesis. (c) The null hypothesis is that the weekly sales are the same and the alternative is that the they are not the same. By using a i test, we do not reject the null hypothesis. (d) The null hypothesis is that the weekly sales are the same and the alternative is that the they are not the same. By using a i test, we reject the…