Question

A recent study at a local college claimed that the proportion, p, of students who commute more than fifteen miles to school is no more than 15%. If a random sample of 275 students at this college is selected, and it is found that 55 commute more than fifteen miles to school, can we reject the college's claim at the 0.1 level of significance? Perform a one-tailed test. Then fill in the table below Carry your intermediate computations to at least three decimal places and round your answers as specified in the table. (If necessary, consult a list of formulas.) The null hypothesis: The type of test statistic: 1 (Choose one) The value of the test statistic: (Round to at least three decimal places.) The critical value at the 0.1 level of significance: Round to at least three decimal places.) Can we reject the claim that the proportion of students who commute more than fifteen miles to Yes No school is no more than 1 5%?

Answer 1

Sol:

Null hypothesis:p $\leqslant$ 0.15

Alternative hypothesis:p>0.15

alpha=0.1

type of statistic:z

test statistic

z=p^-p/sqrt(p*(1-p)/n

p^=sample proportion calculated as=x/n=55/275=0.2

z=0.2-0.15/sqrt(0.15*(1-0.15)/275)

z=2.322

value of test statistic:z=2.322

critical value==NORM.S.INV(0.1)=1.28155=1.282

critical value=1.282

since test statistic >critical value

Reject Ho

YES

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