Question

A recent survey stated that 45% of pet owners talk to their pets on the telephone. A veterinarian believes that the proportion should be lower than the survey's claim. In a random sample of 170 pet owners, 42.9% of them said they spoke to their pets on the telephone. Find the following while performing a hypothesis test to see if there is sufficient evidence that the proportion of pet owners that talk to their pets on the telephone is lower than the survey's claim. Use a significance level of α = 0.05.

a) State the null and alternative hypotheses.

b) z-test statistic. Round the standard deviation to 5 decimal places and the answer to 3 decimal places.

c) p-value

d) State if we would Fail to reject or Reject the null hypothesis.

Answer 1

Solution :

This is the left tailed test .

The null and alternative hypothesis is

H0 : p = 0.45

Ha : p <0.45

n = 170

= 0.429

P0 = 0.45

1 - P0 = 1 - 0.45 =0.55

Test statistic = z

= - P0 / [P0 * (1 - P0 ) / n]

= 0.429 - 0.45/ [(0.45*0.55) / 170 ]

= -0.55

Test statistic = z =-0.55

P(z < -0.55 ) = 0.2912

P-value = 0.2912

= 0.05

P-value >

0.2912 > 0.05

Fail to reject the null hypothesis .

There is insufficient evidence to suggest that