Question

We take a random sample of 250 Canadians and ask them whether they attend a place
of worship (church, temple, mosque, synagogue, etc.). We would like to conduct a
hypothesis test of H0: p = 0:3333 vs. Ha: p < 0:3333 to determine if there is evidence
that less than one-third of Canadians attend a place of worship. It is decided that H0
will be rejected if ^p 0:2892. The level of signicance of the test is closest to:

Answer 1

Solution:

n = 250

The hypothesis for testing the population proportion are

H0: p = 0:3333 vs. Ha: p < 0:3333

Left tailed test.

Let   be the sample proportion.

=0.2892

The test statistic z is

z =   

=  (0.2892- 3333 )/[3333 *(1 - 3333 )/250]

= -1.48

Now, foe left tailed test , the p value is

p value = P(Z < -1.48) = 0.0694

It is given that , the null hypothesis is rejected.

The null hypothesis is rejected when p value is less than the significance level.

So , here , the significance level is larger than the p value.

It may be 0.07 or 0.08 or 0.09 or 0.10

We generally use 0.01 , or 0.05 or 0.10

So , here , the significance level is 0.10