7. [18 points] The following problems are to be approached with the concepts of

Question

7. [18 points] The following problems are to be approached with the concepts of hypothesis testing. In answering each part of this question, identify: . A complete hypothesis statement (i.e. Step 2 of hypothesis testing procedure), using appropriate parameters and values. The required test statistic equation (equation only, eg."Ze The required critical value reference (variable with proper subscripts only, eg-zan). NOTE: You are NOT being asked to calculate the test statistic, nor are you being asked to perform the table lookup sypothesls Test Statsic Criical Value a. A machine in a certain factory must be repaired if it produces more than 10% defectives among the large lot of items it produces in a day. A random sample of 100 items from the day's production contains 15 defectives, and the foreman says that the machine must be repaired. Does the sample evidence support his decision at the 0.01 significance level? b. A corporation sets its annual budget for a new plant on the assumption that the average weekly cost for repairs is to be $1,200. To see whether this claim is realistic, 10 weekly repair cost figures are obtained from similar plants. The sample is assumed to be random and yields an average of $1,290 and standard deviation of S110. Does this sample indicate that $1,200 is not a good assumed value for the mean weekly cost of repairs at a 95% confidence level? Assume normality of weekly repair costs c. A study was conducted to compare the length of time it took men and women to perform a certain assembly-line task. Independent random samples of 50 men and 50 women were employed in an experiment in which each person was timed (in seconds) on identical tasks. The results were Imen 42, smen = 18, Rwomen-38, swomen-14. Do the data present sufficient evidence to suggest a difference between the true mean completion times of this task for men and women? Use a 5% significance level. d. A vice-president for a large corporation claims that the average number of service calls on equipment sold by that corporation is no more than 15 per week To investigate her claim, service records were checked for n=36 randomly selected weeks, of which the sample averaged 17 calls per week and had a standard deviation of 3 calls per week. Does the sample evidence contradict the vice-president's claim at the 5% significance level?

Explanation / Answer

1)

given that
p = 0.10
pht = 15/100 = 0.15
n = 100

The hypothesis is
H0 : machine must not be repaired
H1: machine must be repaired

as the sample size is 100, which is greater than 40 , hence we conduct a z test for proportions as

z = (phat- p)/sqrt(p*(1-p)/n)
so

(0.15-0.1)/sqrt(0.1*0.9/100)

= 1.66 , the test statistics

now we check the z table for the alpha = 0.01 the critical value is
-2.3263

as the z stat > z critical hence we reject the null hypothesis and conclude that
machine must be repaired

Please note that we can answer only 1 question at a time as per the answering guidelines

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