Question

a moving company claims that 95% of its customers are happy with its service. suspecting that it is less, a consumer group surveys 400 customers of the company and finds that 30 of them are actually not happy about the service. set up the null and alternative hypotheses to test for the company’s claim. \\(\circ\\) \\(\text{h}_0: \hat{p} = 0.95\\) \\(\text{h}_\text{a}: \hat{p} > 0.95\\) \\(\circ\\) \\(\text{h}_0: p = 0.95\\) \\(\text{h}_\text{a}: p \
eq 0.95\\) \\(\circ\\) \\(\text{h}_0: p = 0.95\\) \\(\text{h}_\text{a}: p > 0.95\\) \\(\circ\\) \\(\text{h}_0: p = 0.95\\) \\(\text{h}_\text{a}: p < 0.95\\)

Explanation:

1. Recall the definitions: The null hypothesis ($H_0$) is a statement of no difference or the claim being tested. The alternative hypothesis ($H_a$) is what we suspect might be true instead of $H_0$.
2. Here, the company claims that the proportion of happy customers $p = 0.95$. So $H_0: p = 0.95$.
3. The consumer group suspects the proportion of happy customers is less than 0.95 (since 30 out of 400 are not happy, so happy proportion is $\frac{400 - 30}{400}=0.925<0.95$). So the alternative hypothesis is $H_a: p < 0.95$.
4. Also, note that we use the population proportion $p$ (not the sample proportion $\hat{p}$) in hypotheses for proportion tests.

Answer:

D. $H_0: p = 0.95$ $H_a: p < 0.95$ (assuming the last option is labeled D, if the options are labeled as per the order: first option is A, second B, third C, fourth D)