A recent study at a local college claimed that the proportion, , of students who

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A recent study at a local college claimed that the proportion, , of students who commute more than fifteen miles to school is no more than . If a random sample of students at this college is selected, and it is found that commute more than fifteen miles to school, can we reject the college's claim at the level of significance?

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 20%. If a random sample of 265 students at this college is selected, and it is found that 60 commute more than fifteen miles to school, can we reject the college's claim at the 0.05 level of significance? Perform a one-tailed test. Then fill in the table below If you do this pro incorrectly 2 more time practice another qu Perom a ords eetast Carry your intermediate computations to at least three decimal places and round your answers as specified in the table. (If nece consult a list of formulas.) The null hpothesis: The type of test statistic: (Choose one) The value of the test statistic: Round to at least three decimal places The critical value at the 0.05 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 school is no more than es 20%; Clear Undo Next >> Explain

Explanation / Answer

Given n=265, phat=55/265=0.208


H0:p=0.15

H1:p<0.15

Type of test statistic:
Z

value of the test statistic:

Z=(phat-p)/[p*(1-p)/n]

=(0.208-0.15)/sqrt(0.15*(1-0.15)/265)

=2.64

p-value: P(Z<2.64)=0.9959 (check standard normal table)

can we reject te claim that the proportion of students who commute more than fifteen miles to school is no more than 15%?

Since the p-value is larger than 0.05, we do not reject Ho.

So we can not conclude that the proportion of students who commute more than fifteen miles to school is no more than 15%

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