Question

1. The National Aeronautics and Space Administration (NASA) buys bolts from two suppliers, and it is very important the mean widths of the bolts received from both suppliers are equal since they must be used interchangeably.  NASA receives a large shipment of bolts from each supplier, and draws a random sample of 49 bolts from each shipment. It wants to test whether the mean width is the same in both shipments.  Suppose that NASA finds the mean width of the bolts taken from one shipment is 14 inches, and that the mean width of the bolts taken from the other shipment is 1.09 inches.  From past experience it is known that the population standard deviation of the widths from the first supplier is .09 inches and from the second supplier is .11 inches.  

1. Should NASA reject the hypothesis that the mean widths are equal if it sets alpha to .01?
2. What is the p-value?

Answer 1

(A) Using TI 84 calculator

press stat then tests then 2-sampZTest

enter the data

press calculate, we get

test statistic = 15.27

z critical value are -2.58 and 2.58 for 0.01 significance level

So, we will reject the null hypothesis as the z statistic is outside critical value range

(b) p value = 0.0000

p value is less than significance level of 0.01, which tells us that the result significant and we reject Ho

We can say that there is sufficient evidence to warrant the rejection of claim that the mean widths are equal