Question

1. Now suppose Joyce doesn't have population standard deviation (perhaps because these are new machines); she only has her sample standard deviation which is 12. Using the same information, (500 grams average, sample mean of 495, sample size of 24), what are the results of Joyce's analysis? (Check all that apply.) You will need to use one of the tables available on Blackboard (knowing which one is part of the question).

   		Fail to reject the null hypothesis.
   		Reject the null hypothesis at 90% confidence.
   		Reject the null hypothesis at 95% confidence.
   		Reject the null hypothesis at 99% confidence.

Answer 1

Answer)

Null hypothesis Ho : u = 500

Alternate hypothesis Ha : u not equal to 500

Now here we have sample s.d so we will use t distribution

Degrees of freedom is = n-1 = 23

For 23 dof and 90% confidence level, critical value t from t table is 1.71

Margin of error (MOE) = t*s.d/√n = 1.71*12/√24 = 4.2

Interval is given by

(Mean - MOE, Mean + MOE)

[490.8, 499.2].

You can be 90% confident that the population mean (μ) falls between 490.8 and 499.2.

This interval does not contain 500

Reject the null hypothesis at 90% confidence