Question

In order to conduct a hypothesis test for the population mean, a random sample of 20 observations is drawn from a normally distributed population. The resulting sample mean and sample standard deviation are calculated as 10.5 and 2.2, respectively. (You may find it useful to reference the appropriate table: z table or t table).

H0: μ ≤ 9.6 against HA: μ > 9.6

a-1. Calculate the value of the test statistic. (Round all intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.)

a-2. Find the p-value.

0.01  p-value < 0.025

p-value < 0.01

p-value  0.10

0.05  p-value < 0.10

0.025  p-value < 0.05

a-3. At the 5% significance level, what is the conclusion?

Reject H0 since the p-value is less than significance level.

Reject H0 since the p-value is greater than significance level.

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

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

a-4. Interpret the results at αα = 0.05.

We conclude that the population mean is greater than 9.6.

We cannot conclude that the population mean is greater than 9.6.

We conclude that the population mean differs from 9.6.

We cannot conclude that the population mean differs from 9.6..

H0: μ = 9.6 against HA: μ ≠ 9.6

b-1. Calculate the value of the test statistic. (Round all intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.)

b-2. Find the p-value.

0.01  p-value < 0.025

0.025  p-value < 0.05

p-value  0.10

p-value < 0.01

0.05  p-value < 0.10

b-3. At the 5% significance level, what is the conclusion?

Reject H0 since the p-value is less than significance level.

Reject H0 since the p-value is greater than significance level.

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

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

b-4. Interpret the results at αα = 0.05.

We conclude that the population mean is greater than 9.6.

We cannot conclude that the population mean is greater than 9.6.

We conclude that the population mean differs from 9.6.

We cannot conclude that the population mean differs from 9.6.

Answer 1

Solution:

a - 1)

t =   = [10.5 - 9.6]/[2.2/20] = 1.830

the value of the test statistic t = 1.830

a - 2)

df = n - 1 = 20 - 1 = 19

One tailed right tailed test . because , there is > sign in HA )

0.025  p-value < 0.05

a -3)

Reject H0 since the p-value is less than significance level.

a - 4)

We conclude that the population mean is greater than 9.6.

b -1)

t =   = [10.5 - 9.6]/[2.2/20] = 1.830

the value of the test statistic t = 1.830

b - 2)

df = n - 1 = 20 - 1 = 19

TWO tailed test . because , there is   sign in HA )

0.05  p-value < 0.10

b -3)

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

b - 4)

We cannot conclude that the population mean differs from 9.6.