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 H1 at the 5% level of significance, since it is a one-tailed test and it is well beyond the 90% confidence limits.
To determine the appropriate conclusion for testing the hypothesis, we need to compare the given 90% confidence interval for the population mean annual salary with the hypothesized value of $50,000.
In this case, the 90% confidence interval is $45,382 to $48,618. Since the hypothesized value of $50,000 is not within this confidence interval, we can conclude that there is evidence to reject the null hypothesis (H0) and support the alternative hypothesis (H1). The null hypothesis assumes that the population mean annual salary is $50,000, while the alternative hypothesis suggests that it is not.
Now, we need to determine the level of significance to make the appropriate conclusion. The 90% confidence interval implies that the significance level is 10% (100% - 90% = 10%).
Therefore, the correct answer is to conclude H1 at the 10% level of significance.