Homework Sourse13 Listed below are ages of actresses and actors at the time
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Listed below are ages of actresses and actors at the time that they won an award for the categories of Best Actress and Best Actor. Use the sample data to test for a difference between the ages of actresses and actors when they win the award. Use a 0.05 significance level. Assume that the paired sample data is a simple random sample and that the differences have a distribution that is approximately normal.
Actress_age Actor_age
17 50
34 40
24 65
59 52
32 38
In this example,?
?d?
is the mean value of the differences d for the population of all pairs of data, where each individual difference d is defined as the actress\'s age minus the actor\'s age. What are the null and alternative hypotheses for the hypothesis test?
H:O ?d is <, or,>, or, =, or not = to, < and eqaul to, or > and equal to 0____
H:1 ?d is <, or,>, or, =, or not = to, < and eqaul to, or > and equal to 0___
Identify the test statistic.
t= ?
(Round to two decimal places as needed.)
Identify the P-value.
P-value= ?
(Round to three decimal places as needed.)
What is the conclusion based on the hypothesis test?
p value is less or greater___?
reject or fail to reject____ HO?
There is or is not____ signifigant evidance to support the claim?
Solution
Listed below are ages of actresses and actors at the time that they won an award for the categories of Best Actress and Best Actor. Use the sample data to test for a difference between the ages of actresses and actors when they win the award. Use a 0.05 significance level. Assume that the paired sample data is a simple random sample and that the differences have a distribution that is approximately normal.
Actressage Actorage
17 50
34 40
24 65
59 52
32 38
Paired t Test
Data
Hypothesized Mean Difference
0
Level of significance
0.05
Intermediate Calculations
Sample Size
5
DBar
-15.8000
Degrees of Freedom
4
SD
20.2657
Standard Error
9.0631
t Test Statistic
-1.74
Two-Tail Test
Lower Critical Value
-2.7764
Upper Critical Value
2.7764
p-Value
0.1568
Do not reject the null hypothesis
In this example,?
?d?is the mean value of the differences d for the population of all pairs of data, where each individual difference d is defined as the actress\'s age minus the actor\'s age. What are the null and alternative hypotheses for the hypothesis test?
H:O ?d is = 0
H:1 ?d is not = 0
Identify the test statistic.
t= ? -1.74
(Round to two decimal places as needed.)
Identify the P-value.
P-value= ?0.157
(Round to three decimal places as needed.)
What is the conclusion based on the hypothesis test?
p value is greater (0.157 >0.05)
fail to reject HO
There is not signifigant evidance to support the claim.
| Paired t Test | |
| Data | |
| Hypothesized Mean Difference | 0 |
| Level of significance | 0.05 |
| Intermediate Calculations | |
| Sample Size | 5 |
| DBar | -15.8000 |
| Degrees of Freedom | 4 |
| SD | 20.2657 |
| Standard Error | 9.0631 |
| t Test Statistic | -1.74 |
| Two-Tail Test | |
| Lower Critical Value | -2.7764 |
| Upper Critical Value | 2.7764 |
| p-Value | 0.1568 |
| Do not reject the null hypothesis |
