Use the same teams and correct data from Supplemental # 1. Use another sheet of

Question

Use the same teams and correct data from Supplemental # 1. Use another sheet of paper for the claims and hypothesis tests. Use the traditional method. Write down the mean and standard deviation of the Western Team. If you calculated incorrectly in Supplemental #1, use the value I wrote down on your Supplemental #1. Round both numbers to one decimal place. Mean _______ Standard Deviation _______ Write down the mean and standard deviation of the Eastern Team.. If you calculated incorrectly in Supplemental #1, use the value I wrote down on your Supplemental #1. Round both numbers to one decimal place. Mean _______ Standard Deviation _______ The average scoring of teams in the NBA is 105.6. Make a claim about your Western team scoring in relation to the entire NBA average scoring. Is the team scoring more, less, the same, or not the same as the NBA average scoring? Test your claim by using the appropriate hypothesis test. Is there enough evidence to support your claim? Use alpha = 0.05. The average scoring of teams in the NBA is 105.6. Make a claim that is different from #3 about your Eastern team scoring in relation to the entire NBA average scoring. Is the team scoring more, less, the same, or not the same as the NBA average scoring? Test your claim by using the appropriate hypothesis test. Is there enough evidence to support your claim? Use alpha = 0.01.

Explanation / Answer

3. Claim :- Western team is scoring more than the average scoring of teams in the NBA.

4. State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: <= 105.6
Alternative hypothesis: > 105.6

Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected if the sample mean is too large.

Formulate an analysis plan. For this analysis, the significance level is 0.05.

Analyze sample data. Using sample data, z statistic test.

z = (x - ) / s = (108 - 110)/12.1 = -0.165

where s is the standard deviation of the sample, x is the sample mean, is the hypothesized population mean.

Here is the logic of the analysis: Given the alternative hypothesis ( > 105.6), we want to know whether the observed sample mean is large enough to cause us to reject the null hypothesis.

The observed sample mean produced a z statistic test statistic of -0.165.
We use the z Distribution Calculator to find P(z < -0.165)

The P-Value is 0.434472.
The result is not significant at p < 0.05

Interpret results. Since the P-value (0.43) is greater than the significance level (0.05), we cannot reject the null hypothesis.

Conclusion. Fail to reject the null hypothesis. We do not have insufficient evidence to prove the claim that the Western team is scoring more than the average scoring of teams in the NBA.

5. The average scoring of Eastern team is equal to the average of NBA scoring.

6. State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: = 105.6
Alternative hypothesis: 105.6

Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the sample mean is too big or if it is too small.

Formulate an analysis plan. For this analysis, the significance level is 0.01.

Analyze sample data. Using sample data, we compute the z statistic test.

z = (x - ) / s = (105.6 - 105.6)/8.4 = 0

where s is the standard deviation of the sample, x is the sample mean, is the hypothesized population mean.

We use the t Distribution Calculator to find P(z < 0)
The P-Value is 1.
The result is not significant at p < 0.01.

Interpret results. Since the P-value (1) is greater than the significance level (0.01), we cannot reject the null hypothesis.

Conclusion. Accept the null hpothesis. We have sufficient evidence to prove the claim that the average scoring of Eastern team is equal to the average of NBA scoring.

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