Question

in order to determine the average price of hotel rooms is Atlanta, a sample of 64 hotels was selected. it was determined that the average price of the rooms in the sample was $ 112. the population standard deviation is known to be $16. It was determined that the average price of the rooms in the sample was $108.50

1. at 90% confidence using the p-value approach, test the hypothesis. what is your conclusion and why?

2. repeat the hypothesis testing with the critical value approach. What is your conclusion any why?

Answer 1

Given that, sample size ( n ) = 64

sample mean = $ 112

population standard deviation = $ 16

The null and the alternative hypotheses are,

Test statistic is,

1) confidence level = 0.90

=> significance level = 1 - 0.90 = 0.10

p-value = 2 * P(Z > 1.75) = 2 * 0.0401 = 0.0802

=> p-value = 0.0802

Since, p-value = 0.0802 <

we reject the null hypothesis ( H₀).

2) critical values at are, Z^* = ± 1.645

Here, test statistic = 1.75 > 1.645

=> we reject the null hypothesis (H₀).