Question

Consider the following hypotheses: H0: μ = 450 HA: μ ≠ 450 The population is normally distributed with a population standard deviation of 78. (You may find it useful to reference the appropriate table: z table or t table) a-1. Calculate the value of the test statistic with x− = 464 and n = 45. (Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.) a-2. What is the conclusion at the 10% significance level? Reject H0 since the p-value is less than the significance level. Reject H0 since the p-value is greater than the significance level. Do not reject H0 since the p-value is less than the significance level. Do not reject H0 since the p-value is greater than the significance level. a-3. Interpret the results at α = 0.10. We conclude that the population mean differs from 450. We cannot conclude that the population mean differs from 450. We conclude that the sample mean differs from 450. We cannot conclude that the sample mean differs from 450.

b-1. Calculate the value of the test statistic with x− = 437 and n = 45. (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.)

b-2. What is the conclusion at the 5% significance level? Do not reject H0 since the p-value is less than the significance level. Do not reject H0 since the p-value is greater than the significance level. Reject H0 since the p-value is less than the significance level. Reject H0 since the p-value is greater than the significance level.

b-3. Interpret the results at α = 0.05. We cannot conclude that the population mean differs from 450. We conclude that the population mean differs from 450. We cannot conclude that the sample mean differs from 450. We conclude that the sample mean differs from 450.

Answer 1

a-1)
Test statistic,
z = (xbar - mu)/(sigma/sqrt(n))
z = (464 - 450)/(78/sqrt(45))
z = 1.2

a-2)
p-value > 0.1

Do not reject H0 since the p-value is greater than the significance level.

a-3)
We cannot conclude that the population mean differs from 450

b-1)
Test statistic,
z = (xbar - mu)/(sigma/sqrt(n))
z = (437 - 450)/(78/sqrt(45))
z = -1.12

b-2)
p-value > 0.1

Do not reject H0 since the p-value is greater than the significance level.

b-3)
We cannot conclude that the population mean differs from 450