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 260students at this college is selected, and it is found that 42 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:	H0:
The alternative hypothesis:	H1:
The type of test statistic:	(Choose one)ZtChi squareF
The value of the test statistic: (Round to at least three decimal places.)
The p-value: (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 15% ?		Yes	No

Answer 1

Answer)

Null hypothesis Ho : P <= 0.15

Alternate hypothesis Ha : P > 0.15

N = 260

First we need to check the conditions of normality that is if n*p and n*(1-p) both are greater than 5 or not

N*p = 260*0.15 = 39

N*(1-p) = 221

Both the conditions are met so we can use standard normal z table to estimate the P-Value

Z test

Test statistics z = (oberved p - claimed p)/standard error

Standard error = √{claimed p*(1-claimed p)/√n

Observed p = 42/260

Claimed p = 0.15

N = 260

Z = 0.52

From z table, P(z>0.52) = 0.3015

As the obtained p-value is > 0.1 (given significance)

We fail to reject the null hypothesis

So, no we cannot reject the claim