Question

A humane society claims that less than 73% of households in a certain country own a pet. In a random sample of 400 households in that country, 284 say they own a pet. At a=0.10, is there enough evidence to support the society's claim? Complete parts (a) through (c) below. (a) Identify the claim and state Ho and H. Identify the claim in this scenario. Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a decimal. Do not round.) O A % of households in the country own a pet. O B. More than % of households in the country own a pet. OC. The percentage households in the country that own a pet is not %. OD. Less than % of households in the country own a pet. Let p be the population proportion of successes, where a success is a household in the country that owns a pet. State H, and HSelect the correct choice below and fill in the answer boxes to complete your choice. (Round to two decimal places as needed.) OAH:p> OB. Hop H: OD. H:P H:02 H:p OC. Hip- Hops H:p> (b) Use technology to find the P-value. Identify the standardized test statistic. (Round to two decimal places as needed.) Identify the P-value (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. the null hypothesis. There enough evidence to the society's claim.

Answer 1

Given : n=400 , X=284 , The estimate of the sample proportion is , $\hat{p}=\frac{X}{n}=\frac{284}{400}=0.71$

(a ) Claim : D. Less than 73% of households in the country own a pet.

E.Hypothesis: $H_0:p\geq 0.73$ Vs

(b) The test statistic is ,

$Z_{stat}=\frac{\hat{p}-p_0}{\sqrt{\frac{p_0(1-p_0)}{n}}}=\frac{0.71-0.73}{\sqrt{\frac{0.73(1-0.73)}{400}}}=-0.90$

The p-value is ,

p-value=$P(Z>|Z_{stat}|)=P(Z>0.90)=1-P(Z\leq 0.90)=0.1841$

The Excel function is , =1-NORMDIST(0.9,0,1,TRUE)

(c) Decision : Here , p-value =0.1841>0.10

Therefore ,

Fail to reject the null hypothesis . There in not enough evidence to support the societ's claim.