Question

Consider the following hypotheses:

H₀: μ = 380
H_A: μ ≠ 380

The population is normally distributed with a population standard deviation of 77. (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−x− = 390 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 αα = 0.10.

• We conclude that the population mean differs from 380.

• We cannot conclude that the population mean differs from 380.

• We conclude that the sample mean differs from 380.

• We cannot conclude that the sample mean differs from 380.

b-1. Calculate the value of the test statistic with x−x− = 345 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?

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

• 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.

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

b-3. Interpret the results at αα = 0.05.

• We conclude that the population mean differs from 380.

• We cannot conclude that the population mean differs from 380.

• We conclude that the sample mean differs from 380.

• We cannot conclude that the sample mean differs from 380.

Answer 1

population standard deviation ( ) = 77

sample size (n) = 45

sample mean () = 390

H0: μ = 380
HA: μ ≠ 380

a-1)

z = 0.87

test statistic = 0.87

a-2)

P-Value = 2* (1 - P(z < 0.87))

using z table we get

P(z < 0.87)= 0.8078

P-Value = 2* (1 - 0.8087)

P-Value = 0.3826

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 380.

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b-1)

population standard deviation ( ) = 77

sample size (n) = 45

sample mean () = 345

H0: μ = 380
HA: μ ≠ 380

a-1)

z = -3.05

test statistic = -3.05

a-2)

P-Value = 2* P(z < -3.05)

using z table we get

P(z < -3.05)= 0.0011

P-Value = 2* 0.0011

P-Value = 0.0022

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

a-3)

We conclude that the population mean differs from 380.