Question

Consider the following hypotheses:

H₀: μ ≥ 208
H_A: μ < 208

A sample of 74 observations results in a sample mean of 202. The population standard deviation is known to be 26. (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 0.10

• p-value < 0.01

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

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 208.

• We conclude that the population mean is less than 208.

• We conclude that the population proportion differs from 208.

• We conclude that the population proportion equals 208.

Answer 1

Given

n = 74

X_bar = 202

= 26

Hypothesis

H0 : 208

H1 : < 208

1) test statistic Z value

z = (x_bar - ​​​​​​) /(/sqrt(n))

= (202-208)/(20/sqrt(74))

z = -1.99

2) p value for Z test statistic is 0.0233

Therefore p value = 0.0233

3) yes, since the p value is less than significance level.

We know that see that p value (0.0233) is less than 0.1 level of significance hence reject null hypothesis.

4) no, since p value is greater than significance level.

We can see that p value (0.0233) is greater than 0.01 level of significance hence do not reject null hypothesis.

5) interpretation :

P value (0.0233) is greater than 0.01 level of significance hence do not reject null hypothesis so we cannot conclude that population Mean is less than 208.