Question

The health of employees is monitored by periodically weighing them in. A sample of 54 employees has a mean weight of 183.9 lb. Assuming that σ is known to be 21.2 lb, use a 0.05 significance level to test the claim that the population mean of all such employees weights is less than 200 lb. Use the critical value method.

Initial Claim:

Null Hypothesis:

Alternative Hypothesis

Test statistic (make sure you state which test statistic that you are using):

Critical Value

Initial conclusion (justify your answer – graphs are acceptable):

Final conclusion:

Answer 1

Initial Claim:- population mean of all such employees weights is less than 200 lb

Null hypothesis

Alternate hypothesis

Test statistic

we will use z test because the population standard deviation is known and sample size is greater than 30

z test statistic =

Critical value for a lest tailed hypothesis at 0.05 significance level is -1.64(using z table)

Initial conclusion:- z test statistic is less than z critical value for a left tailed hypothesis, which means that the result is significant and we can reject the null hypothesis

Final conclusion:- Since the result is significant, we can say that there is sufficient evidence to conclude that the population mean of all such employees weights is less than 200 lb