Question

Please answer all of my questions

In the problems below, give a complete hypothesis test for each problem. Make sure you include the original claim in symbols, The null and alternative hypothesis, the significance level, the actual formula and calculation of the test statistic, give the p-vale or and drawing of distribution and region. Also include the decision concerning the null hypothesis and a conclusion stated in non-technical terms

1. You are concerned about the high cost of textbooks. You take a random sample of 16 new textbooks in the college bookstore and get a mean of $290.41 with a standard deviation of $39.10. Test the claim at the 0.05 significance level that the average price of textbooks at the college bookstore is less than $200. Assume normality

2. You work at a manufacturing plant and want to improve the average time needed to create and package a rocking chair. Based on previous information you know the time needed to create and package the chair is normally distributed with a mean of 13.5 hours and a standard deviation of 75 hours.   

1. What percentage of chairs would take less than 12 hours to complete? What percentage of chairs would take more than 15 hours to complete? If a chair takes 9 hours or less to complete is this unusual? Justify this answer
2. You take a sample of 50 times needed to create and package this chair and find the average is 13 hours. Would it be unusual for you to find an average time less than or equal to 13 hours? Explain fully
3. You would like to offer a bonus if the 50 workers on a shift would adopt a new process improve the average production time. You want this average to be at the tenth percentile. What amount of time is the tenth percentile?

Answer 1

Let X denote the cost price of textbooks. Under the consideration of normal population for cost of books, we want to test regarding the average population cost, .

We want to perform the test with significance level 0.05.

test statistic=

Since p-value=1, we cannot reject null hypothesis.

We can conclude that we have enough evidence to say the claim regarding average cost price is false.

Let Y denote the time needed to create and package a chair.

a)P(Y<12)=0.492. Hence required percentage=0.492*100%=49.2%

P(Y>15)=0.492. Hence required percentage=0.492*100%=49.2%

P(Y<9)=0.476. the probability is not small rather quite close to 0.50. Hence it is not unusual to take 9 hours or less.

b)

, which is close to 0.50, hence it is not so unusual to find an average time less than or equal to 13 hours.

c)thenth percentile of the sampling distribution of sample mean=0