julian is a manager at a clothing store for teens. he is analyzing the order for next season. data for the…

julian is a manager at a clothing store for teens. he is analyzing the order for next season. data for the previous 10 years suggests that teens are willing to spend an average of $75 for a pair of designer jeans with a standard deviation of $5. however, julian thinks the average may have changed due to a recession. he finds that the last three seasons of data show that teens spent an average of $68 on a pair of jeans. therefore, he performed a hypothesis test to see if the recent average is the same. julian used a significance level of 5% to perform the test. which of the following statements is valid based on the results?\njulians data shows that the recent seasons average jean price is not $75.\njulians data shows that he should order fewer jeans than before.\njulians data shows that the recent seasons average jean price is still $75.\njulians data is inconclusive, so he should order the same number of jeans.

julian is a manager at a clothing store for teens. he is analyzing the order for next season. data for the previous 10 years suggests that teens are willing to spend an average of $75 for a pair of designer jeans with a standard deviation of $5. however, julian thinks the average may have changed due to a recession. he finds that the last three seasons of data show that teens spent an average of $68 on a pair of jeans. therefore, he performed a hypothesis test to see if the recent average is the same. julian used a significance level of 5% to perform the test. which of the following statements is valid based on the results?\njulians data shows that the recent seasons average jean price is not $75.\njulians data shows that he should order fewer jeans than before.\njulians data shows that the recent seasons average jean price is still $75.\njulians data is inconclusive, so he should order the same number of jeans.

Answer

Answer:

Julian's data shows that the recent seasons’ average jean price is not $75.

Explanation:

Step1: Set up hypotheses

$H_0:\mu = 75$, $H_1:\mu\neq75$

Step2: Consider significance level

Significance level $\alpha = 0.05$

Step3: Analyze sample data

Sample mean $\bar{x}=68$, population standard - deviation $\sigma = 5$ (assume normal distribution for large - enough sample or known population std dev). The sample mean of $68$ is quite different from the hypothesized mean of $75$.

Step4: Make conclusion

With a significant difference between the sample mean and the previous average, at a 5% significance level, we reject the null hypothesis $H_0$. So the recent seasons’ average jean price is not $75$.