Question

Assume that a simple random sample has been selected from a normally distributed population and test the given claim. Identify the claim, the null and alternative hypotheses, test statistic, critical value(s), P-value and compare to alpha, and state the final conclusion that addresses the original claim.
INCLUDE A DRAWING OF THE NORMAL CURVE THAT SHOWS THE LOCATION OF THE CRITICAL AREAS AND THE LOCATION OF THE TEST STATISTIC. DO THIS FOR PROBLEMS 1 – 5.

2. (40 points) A golf association requires that golf balls have a diameter of 1.68 inches. To determine if the golf balls conform to the standard, a random sample of golf ball was selected. The diameters are listed below. Do the golf balls conform to the standard at a 99% confidence level?

1.686 1.685 1.684 1.685 1.676 1.678 1.685 1.688 1.689 1.687 1.673 1.673

Steps Included in Hypothesis Testing

Statement of the claim.

___________________________________________________________________________________________

H0: ______________________________

H1: ______________________________
Determine the distribution that will be used: normal z distribution, or the student t distribution.

_________________________________________________________________________________________
Draw the graph of the distribution and identify the critical values based on the confidence level. Shade critical region.

Calculate the test statistic and locate it on the graph drawn in step above.

Use your calculator to determine the P-Value. Compare the P-Value to α
Based on the results of the above two steps: reject the null hypothesis or fail to reject the null hypothesis

MOST IMPORTANT: State in simple nontechnical terms a final conclusion that addresses the original claim.

____________________________________________________________________________________________ ____________________________________________________________________________________________

Answer 1

2.

Suppose, random variable X denotes diameter of golf balls.

Hypothesis-

We have to test for null hypothesis

against the alternative hypothesis

Distribution-

We do not know population standard deviation or population variance. So we have to use student t distribution.

Graph and critical region-

Level of significance

Degrees of freedom

So, critical values are  -3.105807 [Using R-code 'qt(0.005,11)'] and 3.105807 [Using R-code 'qt(0.995,11)'].

The graph with critical values and the critical region (shaded in red colour) is as follows.

Test statistic-

Our test statistic is given by

where,

Location of test statistic-

The position of test statistic (in the previous graph) is as follows.

P-value and comparison-

P-value corresponding to test statistic is given by 0.1761242.

Decision-

We reject the null hypothesis if .

But here we see and so we cannot reject our null hypothesis.

Conclusion-

Based on the given data, we conclude that the golf balls conform to the standard.