1. Consider the following proportion hypothesis:

Give: H_o: p 0.6

H₁: p > 0.6

A binomial distribution can be approximated with the normal distribution, so use a z-score for=0.05.

Test the above hypothesis is a random sample of 250 users has 210 successes.

Solution: [1 point for writing rules/formula]

Calculate :

CalculateZ_p:

Find Z:

CompareZ_p and Z:

Your conclusion:

2. Suppose we fail to reject Ho: 50When the true mean is = 53

Given a sample of size n=64 and =6 and with =0.05

Calculate the critical sample mean X, theZ_{X ,}The probability of type II error and the power of the hypothesis test P.

Solution: [1 point for writing rules/formula]

Calculate X:

Calculate Z_Xwith the true mean = 53:

The probability of type II error :

The power of the hypothesis test P: