Hint: In the following problems, make sure to carefully decide whether using the

Question

Hint: In the following problems, make sure to carefully decide whether using the Z-distribution or t-distribution is more appropriate!

1. A sample of seven days of Papa John’s sales found they sold an average of 34.6 pizzas per day and a sample standard deviation of 12.9. A a sample of ten days of Pizza Hut salesfound they sold an average of 30.2 pizzas per day and a sample standard deviation of 13.3. It is claimed that Papa John’s sells more pizzas on average each day than Pizza Hut. Use df=13 if required.

(a) Complete a six-step hypothesis test to test the claim at = 0.05.

(b) Construct a two-sided 90% condence interval for the dierence in means.

(c) Verify the degrees of freedom that should be used is 13.

Explanation / Answer

Ho : miu 1 = miu 2

H1 : miu1 > miu 2

crtitical value : 1.771

t = ( 34.6 - 30.2) / srqt ( 12.9^2 / 7 + 13.3^2 / 10 )

t = 0.68

since t < critical value we fail to reject Ho

alpha / 2 = 0.05   t =1.771

34.6 - 30.2 +/- 1.771 * srqt ( 12.9^2 / 7 + 13.3^2 / 10 )

4.4 +/- 11.4036

-7.0036 < miu1-miu2 < 15.8036

c)

df = 7 + 10 -2 = 15

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