QUESTION 12 Historically, the proportion of students entering a university who f

Question

QUESTION 12

Historically, the proportion of students entering a university who finished in 4 years or less was 72%. To test whether this proportion has decreased, 130 students were examined and 65% had finished in 4 years or less. Therefore, the test statistic is -1.78. To determine whether the proportion of students who finish in 4 year or less has statistically significantly decreased (at the 5% level of signficance), what is the p-value? (please round your answer to 4 decimal places)

QUESTION 13

A local company is considering introducing incentives to try to get their employees to improve their health. Obviously, the program of incentives costs money, but if they are successful then the company’s health insurance costs will be reduced. Historically, the percentage of the company's employees that are overweight has been 65%. The company’s executives have determined that if they can reduce the percentage of employees who are overweight/obese by 10% then the program is worth the cost. After a year long pilot program a sample of 68 employees revealed that 33 employees in the sample were overweight. When testing the hypothesis that the proportion of overweight employees is less than 55% (using a 5% level of significance), what is the null and alternative hypothesis?

Explanation / Answer

12.

"To determine whether the proportion of students who finish in 4 year or less has statistically significantly decreased", means it is left tailed (by "decreased").

As z = -1.78, by table/technology, the left tailed area is

P(x<-1.78) = Pvalue = 0.0375 [ANSWER]

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13.

After a year long pilot program a sample of 68 employees revealed that 33 employees in the sample were overweight. When testing the hypothesis that the proportion of overweight employees is less than 55% (using a 5% level of significance), what is the null and alternative hypothesis?

Hence, as we test if the proportion is LESS THAN 55%, that is the alternative,

Ho: p >= 0.55
Ha: p < 0.55 [ANSWER]

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