Question

Consider the following hypotheses: H0: μ ≥ 208 HA: μ < 208 A sample of 80 observations results in a sample mean of 200. The population standard deviation is known to be 30. (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. 0.05 p-value < 0.10 p-value 0.10 p-value < 0.01 0.01 p-value < 0.025 0.025 p-value < 0.05 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 = 0.05? Yes since the p-value is less than the significance level. Yes since the p-value is greater than the significance level. No since the p-value is less than the significance level. No since the p-value is greater than the significance level. d. Interpret the results at α = 0.05. We conclude that the population mean is less than 208. We cannot 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

The statistical software output for this problem is:

One sample Z summary hypothesis test:
μ : Mean of population
H₀ : μ = 208
H_A : μ < 208
Standard deviation = 30

Hypothesis test results:

Mean	n	Sample Mean	Std. Err.	Z-Stat	P-value
μ	80	200	3.354102	-2.3851392	0.0085

Hence,

a - 1) Test statistic = -2.39

a - 2) p - value < 0.01

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

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

d) We conclude that the population mean is less than 208.