Question

Exercise 9-15 Algo

Consider the following hypotheses:

H₀: μ ≥ 191
H_A: μ < 191

A sample of 61 observations results in a sample mean of 187. The population standard deviation is known to be 17. (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.
  

• p-value < 0.01

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

b. Does the above sample evidence enable us to reject the null hypothesis at α = 0.05?
  

• 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 191.

• We conclude that the population mean is less than 191.

• We conclude that the population proportion differs from 191.

• We conclude that the population proportion equals 191.

Answer 1

The null and alternative hypothesis is ,

The test is one-tailed test.

Since , the population standard devition is known.

Therefore , use notmal distribution.

a-1)

The value of the test statistic is ,

b-2)

The p-value is ,

p-value=

; From standard normal distribution table

Now ,

0.025 < p-value < 0.05

b. For =0.05

Since , p-value is less than the significance level 0.05

Therefore ,

Yes. the sample evidence enable us to reject the null hypothesis.

c. For =0.01

Since , p-value is greater than the significance level 0.01

Therefore ,

No. the sample evidence does not enable us to reject the null hypothesis.

d. Interpretation :

At the =0.01

We cannot conclude that the population mean is less than 191.