Question

Use 4 decimal places in your calculations. Final answers may be approximated to 2 decimal places.

1. A candy company sells bags of candy that are supposed to have an average of 40 pieces per
bag, with σ = 9 . A random sample of 94 candy bags shows the average number of candies per box
to be 43.1. Using a 1% level of significance, test that the average number of candies per bag is more
than 40.
a. State the null and alternate hypotheses.
b. Determine the p-value.
c. Interpret your results. Can you conclude that the average number of candies per bag is
more than 40? Explain.

Answer 1

Solution :

This is the right tailed test .

The null and alternative hypothesis is ,

H₀ :   = 40

H_a : > 40

Test statistic = z

= ( - ) / / n

= (43.1 - 40) / 9 / 94

= 3.34

P(z > 3.34) = 1 - P(z < 3.34) = 0.0004

P-value = 0.0004

= 0.01

P-value <

Reject the null hypothesis .

There is sufficient evidence to conclude that the average number of candies per bag is more than 40 .