Question

Suppose that a university's toilet paper expenditure per week is a random variable X that has a Normal distribution with mean and standard deviation of 40 rolls.

You want to contrast:

Ho: u = 150 vs Ha: u is not equal to 150.

Suppose that a p-value of 3.156% was obtained for a random sample of 20 weeks.

Choose the best approximation of the observed value of the test statistic that gave rise to such a p-value.

A)101.12

B)135.57

C)130.76

D)160.46

Answer 1

The distribution follows normal and we are testing for population mean. So we will use z-test where the observed value is the sample mean.

Test Stat =

n = 20   = ? = 40

p-value = 2P(Z > T.S.) ..........p-value is the probability so we will find the z-score then equate to the test stat.

1 - P( Z < T.S.) = 0.01578

P( Z < T.S.) = 0.98422

Corresponding z-score = -2.1499 ...............using normal percentage tables

= -2.1499

= -2.1499

= 130.77

Ans: C)130.76

The observed value should be close to the population mean.