Question

A humane society center claims that less than 63% of households in a certain country own a pet. In a random sample of 400 households in that country, 236 say that they own a pet. At α=0.0​1, is there enough evidence to support the society's center's claim? Complete parts​ (a) through​ (d) below.

(a) Identify the claim and state H0 and Ha.

Let p be the population proportion of​ successes, where a success is a household in the country that owns a pet. State H0 and Ha. Select the correct choice below and fill in the answer boxes to complete your choice.

(b) Use technology to find the P-value

Identify the standardized test statistic.

z=

(Round to two decimal places as needed.)

Identify the P-value.

P=

(Round to three decimal places as needed.)

(c) Decide whether to reject or fail to reject the null hypothesis and (d) interpret the decision in the context of the original claim.

[Fail to reject] or [Reject] the null hypothesis. There [is] or [is not] enough evidence to [reject] or [support] the researcher center's claim.

Answer 1

(A) Given claim is that less than 63% of households in a certain country own a pet.

so, we have population proportion po =63/100 = 0.63

"Less than" condition shows that it is a left tailed hypothesis test

(B) Using TI 84 calculator

press stat then tests then select 1-PropZtest

enter the data

po = 0.63

x = 236

n = 400

prop < po

press ENTER, we get

z = -1.66

p value = 0.048

(C) We can see that the probability value is greater than significance level of 0.01, so we failed to reject the null hypothesis

(D) We have failed to reject the null hypothesis. So, we can write it as

Fail to reject the null hypothesis. There is not enough evidence to support the researcher center's claim.