Question

Consider the following hypotheses:

H₀: μ = 450
H_A: μ ≠ 450

The population is normally distributed with a population standard deviation of 48. (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− = 476 and n = 75. (Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.)
  

a-2. What is the conclusion at the 5% 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.

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

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

a-3. Interpret the results at αα = 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.

b-1. Calculate the value of the test statistic with x−x− = 437 and n = 75. (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 1% 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 αα = 0.01.

• 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

Solution :

= 450

= 476

= 48

n = 75

This is the two tailed test .

The null and alternative hypothesis is ,

H₀ :   = 450

H_a :    450

1 ) Test statistic = z

= ( - ) / / n

= (476- 450) /48 / 75

= 4.69

P(z > 4.69) = 1 - P(z <4.69 ) = 0

P-value = 0

=0.05

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

3) We conclude that the population mean differs from 450.

b.1)

= 437 ,n = 75

Test statistic = z

= ( - ) / / n

= (437- 450) /48 / 75

= - 2.345

P(z > -2.345) = 1 - P(z < -2.345 ) = 0.0019

P-value = 0.019

=0.01

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

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