Question

Exercise 9-15 Algo

Consider the following hypotheses:

H₀: μ ≥ 130
H_A: μ < 130

A sample of 74 observations results in a sample mean of 125. The population standard deviation is known to be 31. (You may find it useful to reference the appropriate table: z table or t table)


a-1. Calculate the value of the test statistic. (Negative value should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.)
  

a-2. Find the p-value.
  

• 0.01 p-value < 0.025
• 0.025 p-value < 0.05
• 0.05 p-value < 0.10
• p-value 0.10

• p-value < 0.01

b. Does the above sample evidence enable us to reject the null hypothesis at α = 0.10?
  

• Yes since the p-value is less than the significance level.

• No since the p-value is greater than the significance level.

• No since the p-value is less than the significance level.

• Yes since the p-value is greater than the significance level.

c. Does the above sample evidence enable us to reject the null hypothesis at α = 0.01?
  

• No since the p-value is greater than the significance level.

• No since the p-value is less than the significance level.

• Yes since the p-value is greater than the significance level.

• Yes since the p-value is less than the significance level.

d. Interpret the results at α = 0.01.

• We cannot conclude that the population mean is less than 130.

• We conclude that the population mean is less than 130.

• We conclude that the population proportion differs from 130.

• We conclude that the population proportion equals 130.

Answer 1

The statistical software output for this problem is :

One sample Z summary hypothesis test: u: Mean of population Ho:u= 130 HA: <130 Standard deviation=31 Hypothesis test results: Meann Sample Mean Std. Err. Z-Stat 125 3.6036768 -1.3874718 P-value 0.0826

a-1)

Test statistics = -1.39

a-2) 0.05 < p-value < 0.10

b)

Yes since the p-value is less than the significance level.

(c)

No since the p-value is greater than the significance level.

(d)

We cannot conclude that the population mean is less than 130.