Answer:
Step-by-step explanation:
Box plot is enclosed.
To find out 5 number summary
3.0, 3.5, 4.5, 5.5, 6.5, 6.5, 7.0, 7.0, 7.0, 7.0, 7.0, 7.5, 8.0, 9.0, 9.0, 9.0, 9.5, 9.5, 9.5, 9.5}
Minimum: 3.0
Quartile Q1: 6.5
Median: 7
Quartile Q3: 9
Maximum: 9.5
Besides we find that
Average (mean): μ=7.25
Absolute deviation: 30.5
Mean deviation: 1.525
Minimum: 3.0
Maximum: 9.5
Variance: 3.7125
Standard deviation σ=1.926
Answer:
Since the calculated values is lower than the critical value we have enough evidence to reject the null hypothesis at the significance level of 2.5% and we can say that the true mean is lower than 36 years old
Step-by-step explanation:
Data given
represent the sample mean
represent the sample standard deviation
sample size
represent the value that we want to test
represent the significance level for the hypothesis test.
t would represent the statistic (variable of interest)
represent the p value for the test (variable of interest)
System of hypothesis
We need to conduct a hypothesis in order to check if the true mean is less than 36 years old, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
The statistic is given by:
(1)
And replacing we got:
Now we can calculate the critical value but first we need to find the degreed of freedom:
So we need to find a critical value in the t distribution with df =21 who accumulates 0.025 of the area in the left and we got:
Since the calculated values is lower than the critical value we have enough evidence to reject the null hypothesis at the significance level of 2.5% and we can say that the true mean is lower than 36 years old