Question

1a. A study of 24 randomly chosen dishwashers in Lincoln finds that the mean repair cost is $92.04, with a sample standard deviation of $12.26. Repair costs are known to be normally distributed. Find a 99% confidence interval for the mean repair cost of all dishwashers in Lincoln. Round the confidence interval values to the same number of decimal places as the sample mean.

1b. In a survey of 240 randomly selected high school wrestlers, 50 were injured during their junior year. Find a 90% confidence interval for the proportion of all high school wrestlers injured during their junior year. Round all proportions to 3 decimal places.

2. Choose ONE of the confidence intervals you found in #1. Write a sentence that gives the practical interpretation of that confidence interval.

3. A quality control inspector claims that over 10% of microwaves need repairs during the first five years of use. A researcher is testing this claim.

a. Write the null and alternative hypotheses, and tell whether the test is left-tailed, right-tailed, or two-tailed.

b. In a random sample of 114 microwaves, 16 needed repairs during the first five years. Find the test statistic.

c. Find the P-value.

d. The level of significance for this hypothesis test is 0.05. Should the researcher reject the null hypothesis or fail to reject the null hypothesis?

e. Write a conclusion in the context of the quality control inspector’s claim about microwaves.

Answer 1

Q 1 ) A) Given that

we want to construct the 99% C.I for mean repair cost of all dishwashers in Licoln

Given that

Sample mean

Sample SD

Sample size = n = 24

Confidence level = C = 0.99

95% C.I for mean is

Where ,

DF = n - 1 = 24 - 1 = 23

tc = 2.807  ..............( From t table )

95% C.I for mean is

Therefore 99% C.I for mean repair cost of all dishwashers in Licoln is ..............(Answer)

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Q1) b)

Given that

sample size = n = 240

Confidence level = C = 0.90

Let x=Number of high school wrestlers injured during their junior year = 50

Thereofore sample proportion is

The 90% confidence interval for the proportion of all high school wrestlers injured during their junior year is

Where

Zc= Critical value of C=1.645 ...............( By using Z table)

we get

The 90% confidence interval for the proportion of all high school wrestlers injured during their junior year is

..........(Answer)

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Q 2) Interpretation for 1b): If we repeatedly perform the experiment large number of times and confidence interval is calculated for each sample then at 90% Confidence level the true proportion of all high school wrestlers injured during their junior year is lies between ..........(Answer)