Question

A company’s management thinks that monthly sales have increased, and now average over £50 per month.

• The distribution is known to be normal.
• We assume σ = 10 is known.
• N = 49
• sample mean = 53.1

Test the claim at the 10% significance level (α=.10).

Answer 1

Solution:

= 10

n = 49

= 53.1

Use = 0.10

Hypothesis are

H0 : = 50 (null hypo.)

H1 :   > 50

The test statistic z is given by

z =

= (53.1 - 50) / (10/49)

= 2.17

Now , observe that ,there is > sign in H1. So , the test is right tailed.

p value = P(Z > z) = P(Z > 2.17) = 1 - P(Z < 2.17) = 1 - 0.9850 = 0.0150

p value is less than = 0.10

Reject H₀

There is sufficient evidence to support the claim that the monthly sales have increased,