A researcher wishes to test the hypothesis that the mean age

A researcher wishes to test the hypothesis that the mean age at first marriage for women in Texas is less than 21.7, In a sample of/45/Texas women, he finds that the average age is 23.9 with a standard deviation of 5. Calculate the test statistic to two decimal places. The manufacturer of Twitchy Energy Drink is doing a quality inspection to make sure that the caffeine content of the drink is meeting specifications of 79.5 mg per can. Suppose a quality inspector takes a sample of size 14 from the production line and finds that the average caffeine content in the sample is 79.2 mg, with a standard deviation of 0.42 mg. Calculate the test statistic for testing the hypothesis that the true mean caffeine content is less than 79.5 mg per can, to two decimal places.

Solution

Q16.

t Test for Hypothesis of the Mean

Data

Null Hypothesis                m=

21.7

Level of Significance

0.05

Sample Size

45

Sample Mean

23.9

Sample Standard Deviation

5

Intermediate Calculations

Standard Error of the Mean

0.7454

Degrees of Freedom

44

t Test Statistic

2.9516

Lower-Tail Test

Lower Critical Value

-1.6802

p-Value

0.9975

Do not reject the null hypothesis

Test statistic =2.95 ( two decimals)

Q17.

t Test for Hypothesis of the Mean

Data

Null Hypothesis                m=

79.5

Level of Significance

0.05

Sample Size

14

Sample Mean

79.2

Sample Standard Deviation

0.42

Intermediate Calculations

Standard Error of the Mean

0.1122

Degrees of Freedom

13

t Test Statistic

-2.6726

Lower-Tail Test

Lower Critical Value

-1.7709

p-Value

0.0096

Reject the null hypothesis

Test statistic = -2.67 ( two decimals)

t Test for Hypothesis of the Mean
Data
Null Hypothesis                m=	21.7
Level of Significance	0.05
Sample Size	45
Sample Mean	23.9
Sample Standard Deviation	5
Intermediate Calculations
Standard Error of the Mean	0.7454
Degrees of Freedom	44
t Test Statistic	2.9516
Lower-Tail Test
Lower Critical Value	-1.6802
p-Value	0.9975
Do not reject the null hypothesis