Question

We would like to determine if there is evidence that the true mean weight of all polar bears in Churchill, Manitoba differs from 1000 pounds. Weights of polar bears in Churchill are known to follow a normal distribution with standard deviation 180 pounds. The mean weight of a random sample of 25 polar bears is calculated to be 1057 pounds. What is the P-value of the appropriate test of significance? Report your answer to 4 decimal places.

Answer 1

Let denote the mean weight of all polar bears in Churchill, Manitoba

Null hypothesis, H​​​​​​0: = 1000

Alternative hypothesis, H​​​​​​a : ≠ 1000

= 180

n = 25

x = 1057

Test statistic, z = = 1.583

The p value of the appropriate test of significance

= P(z > 1.583) = 0.0567

Since the p value is greater than 0.05, we fail to reject the null hypothesis