a manager of a grocery store wants to determine if consumers are spending more than the national average…

a manager of a grocery store wants to determine if consumers are spending more than the national average. the national average is $150.00 with a standard deviation of $30.20. the manager collects 40 random receipts and finds that the average is $160. complete a hypothesis test with a significance level of 2.5% to determine if the average customer spends more in his store than the national average. which of the following is a valid conclusion for the manager based on this test?\n\nthe customers spend more than the national average in his store.\nthe manager should decrease prices in his store.\nthe customers do not spend more than the national average in his store.\nthe customers in his store just come from a rich neighborhood.

a manager of a grocery store wants to determine if consumers are spending more than the national average. the national average is $150.00 with a standard deviation of $30.20. the manager collects 40 random receipts and finds that the average is $160. complete a hypothesis test with a significance level of 2.5% to determine if the average customer spends more in his store than the national average. which of the following is a valid conclusion for the manager based on this test?\n\nthe customers spend more than the national average in his store.\nthe manager should decrease prices in his store.\nthe customers do not spend more than the national average in his store.\nthe customers in his store just come from a rich neighborhood.

Answer

Explanation:

Step1: State the hypotheses

$H_0:\mu\leq150$ (null hypothesis), $H_1:\mu > 150$ (alternative hypothesis)

Step2: Calculate the test - statistic

The formula for the z - test statistic in a one - sample z - test is $z=\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}}}$. Given $\bar{x} = 160$, $\mu = 150$, $\sigma=30.20$, and $n = 40$. $z=\frac{160 - 150}{\frac{30.20}{\sqrt{40}}}=\frac{10}{\frac{30.20}{6.3246}}\approx\frac{10}{4.7749}\approx2.09$.

Step3: Find the critical value

For a one - tailed test with a significance level of $\alpha = 0.025$, the critical value $z_{\alpha}=1.96$.

Step4: Make a decision

Since the calculated z - value ($z = 2.09$) is greater than the critical value ($z_{\alpha}=1.96$), we reject the null hypothesis.

Answer:

The customers spend more than the national average in his store.