Last year, 30 % of all employees at a large company enrolled in at least one wel
ID: 3072886 • Letter: L
Question
Last year, 30 % of all employees at a large company enrolled in at least one wellness class at the company's site. A survey is sent out to a sample employees at the start of the new fiscal year to see if a greater percentage is planning to take a wellness class this year. Survey responses are received from 285 employees and 105 indicate that they plan to enroll in a wellness class. Test the appropriate hypotheses using a significance level of 0.10 . Ho: Select an answer v H: Select an answer ? decision rule: reject Ho if probability ? o . Test Statistic: z (Note: round the z-score to two decimal places carry at least four decimal places throughout all of your calculations) probability- probability to four decimal places) decision: select an answer (Note: round the . Conclusion: At the 0.10 level, there Select an answer y significant evidence to conclude the percentage of employees that plan to enroll in at least one wellness class in the upcoming year is Select an answer than 30%.Explanation / Answer
Solution:-
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: P < 0.30
Alternative hypothesis: P > 0.30
Note that these hypotheses constitute a one-tailed test.
Formulate an analysis plan. For this analysis, the significance level is 0.10. 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 (S.D) and compute the z-score test statistic (z).
S.D = sqrt[ P * ( 1 - P ) / n ]
S.D = 0.02714
z = (p - P) / S.D
z = 2.52
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 2.52.
Thus, the P-value = 0.006
Interpret results. Since the P-value (0.006) is less than the significance level (0.10), we cannot accept the null hypothesis.
Reject the null hypothesis.
At 0.10 level, there is significant evidence to conclude the percentage of employees that plan to enroll in atleast one wellness class in the upcoming year is greater than 30%.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.