Question

One-sample t:

Suppose you are a big fan of world cup soccer and want to know if the soccer ball that is going to be used in the next world cup is a different weight than the balls used in the last world cup.

a. Would you formulate this as a one or two sided hypothesis test?

Suppose the average weight of the ball used in the last world cup was 500g.

b. State the null and alternative hypotheses for the weight of the new balls to be used in the next world cup.

You go out and randomly sample the weight of five balls: 502g,501g,495g,492g,491g.

a. what is the mean of your sample?

b. what is the standard deviation of your sample?

c. degrees of freedom?

d. assume the null hypothesis is true and compute the t-statistic based on your dats.

e. what is the probability that the null hypothesis is true(p-value)?

f. would you accept of reject the null at an alpha level of 0.05?

Answer 1

n = 5

S = 5.0695

a) two sided hypothesis test

b) Null and alternative hypothesis is

Level of significance = 0.05

a) sample mean =

b)  standard deviation = S = 5.0695

c) degrees of freedom = n - 1 = 5 - 1 = 4

d)

Test statistic is

e)

Degrees of freedom = n - 1 = 5 - 1 = 4

P-value = 0.1690 ( using t table)

f)

P-value ,Failed to Reject H0

We accept null hypothesis at alpha level of 0.05

conclusion : There is sufficient evidence to support the claim that the average weight of the ball used in the last world cup was 500g.