# Null hypothesis, decision rule, two-tailed test, z value

6

Marks: 1 Please answer questions 6 - 9 based on the following information.

A firm has an order process time of at least 20 minutes. After a change in the process, a researcher wishes to determine if the processing time for orders in a warehouse averages less than 20 minutes, at a 99% confidence level. The researcher uses a sample of 80 orders from a monthly run of 10,000 orders and determines a sample mean of 19 minutes with a standard deviation of 3 minutes.

The null hypothesis is:

Choose one answer.

a. H1 : μ = 20 minutes

b. H0 : μ = 20 minutes

c. H0 : μ >20 minutes

d. H0 : μ <20 minutes

..

7

Marks: 1 This is an example of a:

Choose one answer.

a. an upper-tailed test.

b. a lower-tailed test.

c. a two-tailed test.

..

8

Marks: 1 The decision rule is:

Choose one answer.

a. Fail to reject H0 if z is between -2.58 and +2.58; reject otherwise.

b. Fail to reject H0 if z is between -1.96 and +1.96; reject otherwise.

c. Fail to reject H0 if z is > +2.33; reject otherwise.

d. Fail to reject H0 if z is < -2.33; reject otherwise.

e. Fail to reject H0 if z is > -2.33; reject otherwise.

..

9

Marks: 1 The researcher should reject the null hypothesis.

Choose one answer.

a. True

b. False

..

10

Marks: 1 Please answer questions 10-12 using the following information.

A sample of 60 observations yields a mean of 160 and a sample standard deviation of 40. A sample of 50 observations of another population yields a mean of 149 and a sample standard deviation of 38. A test at the α = 0.05 level of significance is performed for

H0 : µ 1≤ µ2 ; H1 : µ1 > µ2 .

This is an example of a(n):

Choose one answer.

a. lower-tailed test.

b. upper-tailed test.

c. two-tailed test.

..

11

Marks: 1 The value of the test statistic and p-value are, respectively,:

Choose one answer.

a. 1.48, 0.0694

b. 1.61, 0.027

c. 1.96, 0.035

d. 2.28, 0.537

..

12

Marks: 1 The results indicate that the null hypothesis should:

Choose one answer.

a. be rejected.

b. not be rejected.

..

13

Marks: 1 Please answer questions 13 and 14 using the following information.

A report indicates that readership of a home improvement magazine is split evenly among men and women. A random sample of 600 subscribers identifies that 330 are women. The results are tested at the ? = 0.05 level of significance that the report is false.

The null hypothesis and computed value for this problem are, respectively,:

Choose one answer.

a. H0 : μ <0.50; z = 0.46

b. H0 : μ = 0.50; z = 1.96

c. H0 : π = 0.50; z = 2.45

d. H0 : μ ≠ 300; z = 2.58

..

14

Marks: 1 We should conclude that the report is false.

Choose one answer.

a. True.

b. False

..

15

Marks: 1 Please answer questions 15 and 16 using the following information.

In a sample of its readership, 144 of 300 readers in one income bracket approved of the editorial positions of a newspaper. In a different income bracket, 224 of 400 readers approved of the editorial positions. The newspaper wishes to determine if there is a significant difference between the approval rates at an α = 0.05 level of significance.

The computed value of z is:

Choose one answer.

a. 1.645

b. 1.96

c. 2.02

d. 2.1

e. 55.55

..

16

Marks: 1 The test results indicate that there is a significant difference between the approval rates of the separate income brackets.

Choose one answer.

a. True

b. False

..

17

Marks: 1 The student t distribution:

Choose one answer.

a. is preferred over the normal distribution for very large size samples.

b. tends to coincide with the normal distribution for large sample sizes.

c. resembles a curve that is heavily skewed to the left.

d. both a and c.

e. none of the above.

..

18

Marks: 1 The student t distribution will tend to lead to less Type I errors for small samples.

Choose one answer.

a. True

b. False

..

19

Marks: 1 For a lower-tailed test, when the sample mean is 50, the null hypothesis mean is 52.5, s = 7 and n = 25; the student t statistic is:

Choose one answer.

a. 2.091

b. -1.79

c. -2.5

d. 1.63

..

20

Marks: 1 For sample A, n = 12 and s2 = 240; for sample B, n = 18 and s2 = 360. The pooled variance of the samples is:

Choose one answer.

a. 20

b. 300

c. 312.86

d. 350.76

e. not calculable without additional data.

..

21

Marks: 1 Please answer questions 21 and 22 based on the following information.

Procedure 1:n = 6; σ= 10; s2 = 8;

Procedure 2:n = 6; σ = 14; s2 = 12;

The number of degrees of freedom for the t statistic is:

Choose one answer.

a. 5

b. 10

c. 11

d. 12

..

22

Marks: 1 The pooled variance and t statistic are, respectively :

Choose one answer.

a. 10; -2.19

b. 12; -0.8

c. 12.5; 1.2

d. 15; 1.0

..

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6

Marks: 1 Please answer questions 6 - 9 based on the following information.

A firm has an order process time of at least 20 minutes. After a change in the process, a researcher wishes to determine if the processing time for orders in a warehouse averages less than 20 minutes, at a 99% confidence level. The researcher uses a sample of 80 orders from a monthly run of 10,000 orders and determines a sample mean of 19 minutes with a standard deviation of 3 minutes.

The null hypothesis is:

Choose one answer.

a. H1 : μ = 20 minutes

b. H0 : μ = 20 minutes

c. H0 : μ >20 minutes

d. H0 : μ <20 minutes

..

7

Marks: 1 This is an example of a:

Choose one answer.

a. an upper-tailed test.

b. a lower-tailed test.

c. a two-tailed test.

Explanation: This is because H1 : μ <20 minutes

8

Marks: 1 The decision rule is:

Choose one answer.

a. Fail to reject H0 if z is between -2.58 and +2.58; reject otherwise.

b. Fail to reject H0 if z is between -1.96 and +1.96; reject otherwise.

c. Fail to reject H0 if z is > +2.33; reject otherwise.

d. Fail to reject H0 if z is < -2.33; reject otherwise.

e. Fail to reject H0 if z is > -2.33; reject otherwise.

..

Explanation:

The rejection region of H0 with 99% confidence level is

Z< - 2.33.

9

Marks: 1 The researcher should reject the null hypothesis.

Choose one answer.

a. True ...

#### Solution Summary

The expert examines null hypothesis, decision rules, two tailed tests and z values.