Last year, 3 1 % of all employees at a large company enrolled in at least one we
ID: 3065275 • Letter: L
Question
Last year, 3 1 % 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 277 employees and 108 indicate that they plan to enroll in a wellness class. Test the appropriate hypotheses using a significance level of 0.05 ·Ho : select an answer vry H Select an answer decision rule: reject H0 ifprobabilityEya Test Statistic: z decimal places throughout all of your calculations) probability = decision: Select an answer Conclusion: At the 0.0S level, there Select an answer 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 answere] than 3 1%. (Note: round the z-score to two decimal places-carry at least four (Note: round the probability to four decimal places)Explanation / Answer
We formulate the null and alternate hypothesis as:
H0: p0 = 0.31 (proportion of Employee enrolling for wellness class is equal to 0.31)
Ha: p0 > 0.31 (proportion of Employee enrolling for wellness class is greater than 0.31)
alpha = 0.05
n = 277
P^ = 108/277 = 0.3899
Right tailed test.
Test Statistic:
z = (P^ - p0)/ (p0 * (1- p0)/n)1/2 = 2.87
using the z critical value at alpha = 0.05 we find zcritical = 1.645
Using the Z-table, we the p-value = 1-.9979 = 0.0021
Since, our z > zcritical, we reject the null hypothesis in favour of alternate hypothesis ie the proportion of Employee enrolling for wellness class is greater than 0.31
Decision: Reject the null hypothesis.
Conclusion: At the 0.05 level, there is significant evidence to conclude the percentage of employees that plan to enrol in at least one wellness class in the upcoming year is more than 31%.
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