Question

Question 1: Test the following hypothesis: H0:μ = 41.8 versus H1:μ > 41.8; y =43.1, n =16, σ = 3.1, α =0.05. Assume that the data comes from a normal distribution. The conclusion is to

- reject the null hypothesis

- fail to reject the null hypothesis

Question 2: (not for forum discussion) Test the following hypothesis: H0:μ = 41.8 versus H1:μ ≠ 41.8; y =43.1, n =16, σ = 3.1, α =0.05. Assume that the data comes from a normal distribution. The conclusion is to

- reject the null hypothesis

- fail to reject the null hypothesis

Answer 1

Solution:

Question 1:

This is a right tailed test.

The test statistics,

Z =( - )/ (/n)

= ( 43.1 - 41.8 ) / ( 3.1 / 16 )

= 1.68

P-value = P(Z > z )

= 1 - P(Z < 1.68 )

= 1 - 0.9535

= 0.0465

The p-value is p = 0.0465, and since p = 0.0465 < 0.05 , it is concluded that the null hypothesis is rejected.

- reject the null hypothesis.

Question 2:

This is a two tailed test.

The test statistics,

Z =( - )/ (/n)

= ( 43.1 - 41.8 ) / ( 3.1 / 16 )

= 1.68

P-value = 2 * P(Z >z )

= 2 * 1 - P(Z < 1.68 )

= 2 * (1 - 0.9535 )

= 2 * 0.0465

= 0.093

The p-value is p = 0.093, and since p = 0.093 > 0.05 , it is concluded that fail to reject the null hypothesis.

- fail to reject the null hypothesis