Question

In: Statistics and Probability

An Office of Admission document at a certain university claims that 55.3% of their undergraduates are...

An Office of Admission document at a certain university claims that 55.3% of their undergraduates are female. To test this claim, a random sample of 220 undergraduates was selected. In this sample, 56.1% were female. Is there sufficient evidence to conclude that the document's claim is false? Carry out a hypothesis test at a 8% significance level.

A. The value of the test statistic is:

B. The p-value is

D. Your decision for the hypothesis test:

A. Reject H0H0.
B. Do Not Reject H1H1.
C. Reject H1H1.
D. Do Not Reject H0H0.

Solutions

Expert Solution

Given that An Office of Admission document at a certain university claims that 55.3% of their undergraduates are female.

So, the Hypotheses are:

Based on the hypotheses it will be a two-tailed test.

Given that a random sample of n=220 undergraduates was selected. In this sample, the sample proportion of =56.1% were female.

Requirements for Hypothesis testing:

The sample is less than 5% of the population also the sample is randomly selected so, the requirement for hypothesis testing is satisfied.

Rejection region:

At 0.08 level of significance reject Ho if |Z|>Z0.04 =1.75 ( Calculated using the Z table shown below or by using excel tool using formula{ =NORM.S.INV(0.96)})

a) Test statistic:

The test statistic is calculated as:

b) P-value:

The P-value is computed using the Z table shown below at Z score calculated above as:

P-value=0.8103

c) Decision:

Since P-value>0.08 and |Z| <Z0.04 =1.75 hence Do not reject the null hypothesis(Ho).

Conclusion:

Since we do not reject the null hypothesis we conclude that there is not sufficient evidence to warrant the claim.

The Z table:

orchestra answered 2 years ago
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