8. a company claims that 40% of its customers prefer home delivery, but a consumer advocacy group suspects the true percentage is smaller than 40%. after collecting data from a random sample of customers and conducting a hypothesis test, the consumer advocacy group reports a p - value of 0.06 using a significance level of 0.05. which conclusion should be reached based on this hypothesis testing result?
a. the observed sample statistic is consistent with the companys claim that 40% of its customers prefer home delivery because 0.06 is greater than 0.05.
b. we have proven that 40% of the companys customers prefer home delivery because 0.06 is larger than 0.05.
c. the null hypothesis is true because 0.06 0.05.
d. the consumer advocacy group must have found that more than 40% of the surveyed sample said they prefer home delivery because the p - value is positive.
e. there is good evidence to suggest the companys claim that 40% of its customers prefer home delivery is false because 0.06 is smaller than 1.

Question

8. a company claims that 40% of its customers prefer home delivery, but a consumer advocacy group suspects the true percentage is smaller than 40%. after collecting data from a random sample of customers and conducting a hypothesis test, the consumer advocacy group reports a p - value of 0.06 using a significance level of 0.05. which conclusion should be reached based on this hypothesis testing result?
a. the observed sample statistic is consistent with the companys claim that 40% of its customers prefer home delivery because 0.06 is greater than 0.05.
b. we have proven that 40% of the companys customers prefer home delivery because 0.06 is larger than 0.05.
c. the null hypothesis is true because 0.06 > 0.05.
d. the consumer advocacy group must have found that more than 40% of the surveyed sample said they prefer home delivery because the p - value is positive.
e. there is good evidence to suggest the companys claim that 40% of its customers prefer home delivery is false because 0.06 is smaller than 1.

Accepted Answer

# Brief Explanations:
In hypothesis testing, if the $P -$value is greater than the significance level ($\alpha$), we fail to reject the null hypothesis. Here, the null hypothesis is the company's claim ($H_0:p = 0.4$) and the alternative hypothesis is $H_1:p<0.4$. The significance level $\alpha = 0.05$ and $P-$value $=0.06$. Since $P-$value $>\alpha$, we do not have enough evidence to reject the null hypothesis.
- Option B is wrong because hypothesis testing does not "prove" a claim, it either provides evidence against  a claim or not.
- Option C is wrong because we do not know if the null hypothesis is "true", we just do not have enough evidence to reject it.
- Option D is wrong because the sign of the $P -$value does not tell us about the sample proportion. The $P -$value is a probability.
- Option E is wrong because comparing the $P -$value to $1$ is not the correct rule (the rule is to compare $P -$value to $\alpha$).

# Answer:
A. The observed sample statistic is consistent with the company’s claim that 40% of its customers prefer home delivery because 0.06 is greater than 0.05.

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