Elementary Statistics ( 3rd International Edition ) Isbn:9781260092561
Elementary Statistics ( 3rd International Edition ) Isbn:9781260092561
3rd Edition
ISBN: 9781259969454
Author: William Navidi Prof.; Barry Monk Professor
Publisher: McGraw-Hill Education
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Chapter 15, Problem 1CQ

a.

To determine

To find:The value of test statistic.

a.

Expert Solution
Check Mark

Answer to Problem 1CQ

The value of test statistic is 2.7 .

Explanation of Solution

Given information:

The data is 50,38,23,29,57,26,53,42,60,23 and the hypothesis are H0:m=30 and H1:m30 .

Concept used:

The test statistic is,

If the sample size is less than or equal to 25 then the test statistic is X .

If the sample size is greater than 25 then the test statics is,

  z=x+0.5n2n2

Here, the number of times the less frequent sign occur is x .

The conditions for test statistics are shown below in table.

    Type of testTest statistic
    Right-tailed testNumber of minus signs
    Left-tailed testNumber of plus signs
    Two-tailed testNumber of plus or minus signs, whichever is smaller

Calculations:

The value of test statistic is shown below.

    SampleDifferenceSigns
    5020-
    388+
    23-7-
    29-1-
    5727+
    26-4-
    5323+
    4212+
    6030+
    23-7-

From the above table, the number of minus sign is 4 and the number of plus sign is 6 and the sample size is 19 .

Since, the sample size is less than 25 .

The test statistic is given by the number of plus or minus sign which are smaller in number.

  x=4

Therefore, the value of test statistic for the given sample is 2 .

b.

To determine

To find:Whether the hypothesis H0 rejected or not.

b.

Expert Solution
Check Mark

Answer to Problem 1CQ

The hypothesis H0 is not rejected.

Explanation of Solution

Given information:

The level of significance is 0.05 .

Calculations:

The critical value for two-tailed test at sample size of 10 and level of significance of 0.05 is 1 .

Since, the test statistics is 4 which greater than the critical value.

Therefore, the hypothesis H0 is not rejected.

c.

To determine

To find:Whether the hypothesis H0 rejected or not.

c.

Expert Solution
Check Mark

Answer to Problem 1CQ

The hypothesis H0 is not rejected.

Explanation of Solution

Given information:

The level of significance is 0.01 .

Calculations:

The critical value for two-tailed test at sample size of 10 and level of significance of 0.01 is 0 .

Since, the test statistics is 4 which greater than the critical value.

Therefore, the hypothesis H0 is not rejected.

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Elementary Statistics ( 3rd International Edition ) Isbn:9781260092561

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