Question

The Nero Match Company sells matchboxes that are said to contain an average of 40 matches per box with a standard deviation of 9 matches. A random sample of 94 Nero matchboxes shows the average number per box to be 41.8 Using a​ 1% level of​ significance, can you say that the average number of matches per box is more than​ 40?

1) What type of hypothesis test is​ this?

​2) State the hypotheses.  

​3) Calculate the value of the Test Statistic.

​4) Calculate the​ P-Value.

​5) What is the​ decision?

Answer 1

n = 94

Sample mean =

Population standard deviation =

Here Population standard deviation is known so we use z test.

1) This is one sample z test.

2) Here we have to test that

where

3) Test statistic:

z = 1.94 (Round to 2 decimal)

Test statistic = 1.94

4) P value:

Test is right tailed test.

P value = P(z > 1.94)

= 1 - P(z < 1.94)

= 1 - 0.9738 (From statistical table of z values)

= 0.0262

P value = 0.0262

5)

Level of significance = = 0.01

Here p value >

So we fail to reject H0.

Conclusion : There is not sufficient evidence to support the claim that the average number of matches per box is more than​ 40