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The proportion of female students at Lehman College is 68%. Suppose there are 145 students enrolled...

The proportion of female students at Lehman College is 68%. Suppose there are 145 students enrolled in some major, of which 113 are female. Can we conclude that there is a higher proportion of female students in this major than at Lehman overall? Use a significance level of 0.01.

(a) What are the null and alternative hypotheses?

(b) What is the test statistic?

(c) What is the critical value?

(d) Do you reject or fail to reject the null hypothesis? Explain your reasoning.

(e) What is the probability of a Type I error?

(f) Can you conclude that there is a higher proportion of female students in this major than at Lehman overall?

Math   Statistics-And-Probability   
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Answer #1

Note that 2.56 > 2.326.

Thus we reject the null hypothesis.

probability of a Type I error = Level of significance = 0.01

Yes, we can conclude that there is a higher proportion of female students in this major than at Lehman overall, because null hypothesis is rejected.

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