The manager of Hudson Auto Repair wants to advertise one price for an engine tun
ID: 3250165 • Letter: T
Question
The manager of Hudson Auto Repair wants to advertise one price for an engine tune up, with parts included. Before he decides the price to advertise, he needs a good estimate of the average cost of tune-up parts. A sample of 10 customer invoices for tune-ups has been taken and the costs of parts, rounded to the nearest to the dollar, are listed below 104 74 62 68 97 73 77 65 80 109 a. Indicate the formula you would use to find the point estimate for the mean cost of parts per tune-up for all the turn-ups. b. Construct a 90% confidence interval estimate of the mean cost of parts per tune-up for all of the tune-ups performed at Hudson Auto Repair. A sample of 16 cookies is taken to test the claim that each cookie contains al least 9 chocolate chips. The average number of chocolate chips per cookie in the sample was 7.875 with a standard deviation of 1. Assume the distribution of the population is normal. a. Stare the null and alternative hypotheses. b. Compute the p-value and test the hypothesis at the 1% level of significance. c. State the conclusion of your test. d. What type of error (type I or II) might you have made?Explanation / Answer
Question 2 is not properly visible so i am doing question number 3 only
a. Null HYpothesis : H0: There are not more than 9 chocolate chips in each cookie. H < 9
Alternative Hypothesis : Ha : There are at least 9 chocolate chips in each cookie. >= 9
b. Test statistic :
t = (xbar- H)/ ( s/n) = ( 7.875 - 9)/ (1/ 16) = -1.125/ (1/4) = -4.5
P - value = 0.9999
c. We can reject the null hypothesis and conclude that there are less than 9 chocolate chips in one cookie.
d. Type I error here is to reject the null hypothesis even it is true that means we can reject the hypothesis that chocolate chips in one cookies are less than 9 in one cookie even if it is more than that.
Type II error here is to failed to reject the null hypothesis even it is false. That means we will say that there are less than 9 chocolate chips in one cookie even in truth, there are more than that in reality.
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