Question

13. You wish to test the claim that fewer than 33% of households in a certain city own pets.

• [3 points] Give the null and alternate hypotheses.

• [2 points] Is the test right-tailed, left-tailed or two-tailed?

• The P-value was found to be 0.0673,

Choose using a significance level of 5%:

Reject the null hypothesis or Fail to reject the null hypothesis

Give the conclusion about the claim in an English sentence in the context of the scenario.

A person wants to open a pet supply store in the city, but not if fewer than 33% of the city’s households have pets, Based on your conclusion, should the person open the store?       

Answer 1

Solution:

Given:

Claim: fewer than 33% of households in a certain city own pets.

Part a) Give the null and alternative hypotheses.

Since claim is directional to left side ( fewer ), thus alternative hypothesis is < type.

Thus:

H0: p 0.33

Vs

H1: p < 0.33

Part b) Is the test right-tailed, left-tailed or two-tailed?

This is left tailed test, since H1 is < type.

Part c) The P-value was found to be 0.0673,

Choose using a significance level of 5%:

Decision Rule:
Reject H0, if P-value < 0.05 level of significance, otherwise we fail to reject H0

Since P-value = 0.0673 > 0.05 level of significance,

we fail to reject null hypothesis H0.

Part d) Give the conclusion about the claim in an English sentence in the context of the scenario.

At 0.05 significance level, we do not have sufficient evidence to support the claim that: fewer than 33% of households in a certain city own pets.

Thus we conclude that: 33% or more of households in a certain city own pets.

Part e) A person wants to open a pet supply store in the city, but not if fewer than 33% of the city’s households have pets, Based on your conclusion, should the person open the store?       

Since we have concluded that 33% or more of households in a certain city own pets, the person should open the store in the city.