A management consultant has analysed a random sample of 40 large firms in order to investigate the mean annual salary of sales managers. She has constructed the following 90% confidence interval for the population mean annual salary: $45,382 to $48,618. In testing the hypothesis that the population mean annual salary is $50,000 she should:

Question 11 options:

Conclude H0 at the 5% level of significance

Conclude H0 at the 10% level of significance

Conclude H1 at the 5% level of significance

Conclude H1 at the 10% level of significance

Conclude H0 at the 5% level of significance

To determine whether to conclude H0 (null hypothesis) or H1 (alternative hypothesis) at a certain level of significance, we need to compare the hypothesized value ($50,000 in this case) with the confidence interval.

In this scenario, the 90% confidence interval for the population mean annual salary is $45,382 to $48,618. Since the hypothesized value of $50,000 is not within this confidence interval, we can conclude H1 (the alternative hypothesis) that the population mean annual salary is not $50,000.

Now, let's address the significance levels mentioned in the answer choices. The significance level determines the probability of rejecting the null hypothesis when it is actually true.

As none of the answer choices specify the significance level as 90%, let's assume the 5% and 10% significance levels are being considered. In both cases, we conclude H1 because the hypothesized value ($50,000) falls outside the confidence interval.

Therefore, the correct answer is: Conclude H1 at the 5% level of significance or Conclude H1 at the 10% level of significance.