Question

A hospital administrator finds that the mean hospital stay for a sample of

86

women after childbirth is

2.9

days. She claims that the mean stay at her hospital is greater than the national average of

2.4

days. Assuming that the average at her hospital is the same as the national​ average, the probability of observing a sample with a mean of

2.9

days or more is

0.17

Formulate the null and alternative hypotheses. Then discuss whether the sample provides evidence for rejecting or not rejecting the null hypothesis. Assume a significance level of

0.05

Identify the hypotheses.

A.Null​ hypothesis: mean

stayequals=2.4

daysAlternative​ hypothesis: mean

stayequals=2.9

days

B.Null​ hypothesis: mean

stayequals=2.4

daysAlternative​ hypothesis: mean

stayless than<2.4

days

C.Null​ hypothesis: mean

stayequals=2.4

daysAlternative​ hypothesis: mean

staygreater than>2.4

days

D.Null​ hypothesis: mean

stayequals=2.4

daysAlternative​ hypothesis: mean

staynot equals≠2.4

daysIs the result of the test statistically significant at the

0.05

​level?

A.The test

is not

statistically significant at the

0.050.05

​level, because the chance of a sample mean at least as extreme as the observed one is

greater

than

0.05​,

assuming the null hypothesis to be true.

B.The test

is not

statistically significant at the

0.05

​level, because the chance of a sample mean at least as extreme as the observed one is

less

than

0.05,

assuming the null hypothesis to be true.

C.The test

is

statistically significant at the

0.05

​level, because the chance of a sample mean at least as extreme as the observed one is

less

than

0.05​,

assuming the null hypothesis to be true.

D.The test

is

statistically significant at the

0.05

​level, because the chance of a sample mean at least as extreme as the observed one is

greater

than

0.05​,

assuming the null hypothesis to be true.

Determine if the null hypothesis should be rejected.

A.

Do not reject

the null hypothesis because the chance of the sample result is

greater

than the significance level.

B.

Do not reject

the null hypothesis because the chance of the sample result is

less

than the significance level.

C.

Reject

the null hypothesis because the chance of the sample result is

greater

than the significance level.

D.

Reject

the null hypothesis because the chance of the sample result is

less

than the significance level.

Answer 1

We want to test the claim that the mean stay is greater than 2.4

Therefore, the hypothesis to tested will be,

Null hypothesis: Mean stay = 2.4

Alternative hypothesis: Mean stay > 2.4 (claim)

Option C

Now, the p value i.e. the probability of observing sample mean >= 2.9 is 0.17, under null hypothesis.

Since, 0.17>0.05, we do not reject null hypothesis. The claim proves to be false/insignificant.

Therefore, the correct option is Option A

And also because we are not rejecting the null hypothesis because Pvalue is greater than significance level(0.05) the correct option is Option A