Narrative: This is based on Section 9.5 of your book and addresses the topic of

Question

Narrative: This is based on Section 9.5 of your book and addresses the topic of testing hypotheses for a population proportion.

Over the past year, 20% of the players at Pine Creek were women. In an effort to increase the proportion of women players, Pine Creek implemented a special promotion designed to attract women golfers. One month after the promotion was implemented, the course man- ager requested a statistical study to determine whether the proportion of women players at Pine Creek had increased. Because the objective of the study is to determine whether the proportion of women golfers increased, an upper tail test with Ha: p > .20 is appropriate.

TASKS:
1) Using Excel, develop a template to compute the p-values for each lower and upper tails and for the 2-tailes test.
2) Using the formula in table 9.4, calculate algebraically (use the spreadsheet) each z-statistic
3) Did Pine Creek succeed in raising its female membership? Test the null hypothesis with =0.05.

Narrative: This is based on Section 9.5 of your book and addresses the topic of testing hypotheses for a population proportion.

Over the past year, 20% of the players at Pine Creek were women. In an effort to increase the proportion of women players, Pine Creek implemented a special promotion designed to attract women golfers. One month after the promotion was implemented, the course man- ager requested a statistical study to determine whether the proportion of women players at Pine Creek had increased. Because the objective of the study is to determine whether the proportion of women golfers increased, an upper tail test with Ha: p > .20 is appropriate.

TASKS:
1) Using Excel, develop a template to compute the p-values for each lower and upper tails and for the 2-tailes test.
2) Using the formula in table 9.4, calculate algebraically (use the spreadsheet) each z-statistic
3) Did Pine Creek succeed in raising its female membership? Test the null hypothesis with =0.05.

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Explanation / Answer

Solution:-

P = 20/100 = 0.20

x = 100, n = 400

p = 100/400

p = 0.25

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

Null hypothesis: P < 0.20

Alternative hypothesis: P > 0.20

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

Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method, shown in the next section, is a one-sample z-test.

Analyze sample data. Using sample data, we calculate the standard deviation () and compute the z-score test statistic (z).

= sqrt[ P * ( 1 - P ) / n ]

= 0.02

z = (p - P) /

z = 2.5

where P is the hypothesized value of population proportion in the null hypothesis, p is the sample proportion, and n is the sample size.

Since we have a one-tailed test, the P-value is the probability that the z-score is greater than 2.5. We use the Normal Distribution Calculator to find P(z > 2.5) = 0.0062

Thus, the P-value = 0.0062

Interpret results. Since the P-value (0.0062) is less than the significance level (0.05), we cannot accept the null hypothesis.

From the above test we have sufficient evidence that proportion of females have increased.

p value for two-tailed test = 0.0062 + 0.0062 = 0.0124

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