Question

 3. Complete the statements: The _______  of the confidence interval is exactly twice that of the _______ . When C increases from 90% to 98%, the width of the interval slightly_______ . When the interval increases, the precision_______  One way to reduce the margin of error is to increase the_______ 

 4. A random sample of the costs of repair jobs at a large muffler repair shop produces a mean of $127.95 and a standard deviation of $24.03. If the size of the random sample is 40, calculate the 90 percent confidence interval for the average cost of the repair at this repair shop. Show all steps including checking conditions, work, and interpretation.

Answer 1

1) This part appears to be connected with different questions as there is no such data to fill the blanks so, I am skipping this part and answering 2nd one.

2). For the given sample with sample size n=40 and Sample mean=127.95also given the sample standard deviation s=24.03.

Since the sample is randomly selected and the sample size is greater than 30 hence both conditions are satisfied for the normality of distribution.

we use T-distribution to calculate the confidence interval because the population standard deviation is unknown.

The tc is the critical t-score at a given level of significance 1-confidence level=1-0.90=0.10, in this case, is calculated by excel at a given confidence level and calculated degree of freedom.

The degree of freedom is calculated as n-1=40-1=39

The formula used to find tc value in excel is =T.INV.2T(0.10,39) which results in tc=1.685

Now the confidence interval is calculated as:

1.685 x 24.03 1.685 x 24.03 40 127.95 + V40 = (127.95 – 6.402, 127.95 + 6.402) = (121.548, 134.352)

Interpretation:

We can be 90% confident that the population mean (μ) falls between 121.548 and 134.352.