question 8
1 pts
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?
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.
we have proven that 40% of the companys customers prefer home delivery because 0.06 is larger than 0.05.
the null hypothesis is true because 0.06 0.05
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.
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

question 8
1 pts
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?
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.
we have proven that 40% of the companys customers prefer home delivery because 0.06 is larger than 0.05.
the null hypothesis is true because 0.06 > 0.05
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.
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 $H_0:p = 0.4$ (where $p$ is the proportion of customers who prefer home - delivery) and the alternative hypothesis $H_a:p<0.4$. The significance level $\alpha = 0.05$ and $P - value=0.06$. Since $P - value(0.06)> \alpha(0.05)$, we do not have enough evidence to reject the null hypothesis. This means the observed sample statistic is consistent with the company's claim. We cannot prove the null hypothesis (hypothesis testing does not prove a hypothesis, it just provides evidence for or against it), and the $P -$value being positive does not imply more than $40\%$ of the sample prefer home - delivery. Also, $P - value<1$ is always true and not a valid reason for rejecting or not rejecting the null hypothesis.

# Answer:
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.

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Answer: