In: Statistics and Probability
You wish to test the following claim (HaHa) at a significance
level of α=0.01α=0.01.
Ho:μ1=μ2Ho:μ1=μ2
Ha:μ1≠μ2Ha:μ1≠μ2...
You wish to test the following claim (HaHa) at a significance
level of α=0.01α=0.01.
Ho:μ1=μ2Ho:μ1=μ2
Ha:μ1≠μ2Ha:μ1≠μ2
You believe both populations are normally distributed, but you
do not know the standard deviations for either. And you have no
reason to believe the variances of the two populations are equal
You obtain a sample of size n1=14n1=14 with a mean of
¯x1=79.7x¯1=79.7 and a standard deviation of s1=11.8s1=11.8 from
the first population. You obtain a sample of size n2=15n2=15 with a
mean of ¯x2=83.8x¯2=83.8 and a standard deviation of s2=19.1s2=19.1
from the second population.
- What is the test statistic for this sample?
test statistic = Round to 3 decimal places.
- What is the p-value for this sample? For this calculation, use
.
p-value = Use Technology Round to 4 decimal
places.
- The p-value is...
- less than (or equal to) αα
- greater than αα
- This test statistic leads to a decision to...
- reject the null
- accept the null
- fail to reject the null
- As such, the final conclusion is that...
- There is sufficient evidence to warrant rejection of the claim
that the first population mean is not equal to the second
population mean.
- There is not sufficient evidence to warrant rejection of the
claim that the first population mean is not equal to the second
population mean.
- The sample data support the claim that the first population
mean is not equal to the second population mean.
- There is not sufficient sample evidence to support the claim
that the first population mean is not equal to the second
population mean.
-
Similarly, you now wish to test the following claim (HaHa) at a
significance level of α=0.10α=0.10.
Ho:μ1=μ2Ho:μ1=μ2
Ha:μ1≠μ2Ha:μ1≠μ2
You believe both populations are normally distributed, but you
do not know the standard deviations for either. And you have no
reason to believe the variances of the two populations are equal
You obtain a sample of size n1=14n1=14 with a mean of
¯x1=59.9x¯1=59.9 and a standard deviation of s1=15.6s1=15.6 from
the first population. You obtain a sample of size n2=10n2=10 with a
mean of ¯x2=51.6x¯2=51.6 and a standard deviation of s2=13.4s2=13.4
from the second population.
- What is the test statistic for this sample?
test statistic = Round to 3 decimal places.
- What is the p-value for this sample? For this calculation, use
.
p-value = Use Technology Round to 4 decimal
places.
- The p-value is...
- less than (or equal to) αα
- greater than αα
- This test statistic leads to a decision to...
- reject the null
- accept the null
- fail to reject the null
- As such, the final conclusion is that...
- There is sufficient evidence to warrant rejection of the claim
that the first population mean is not equal to the second
population mean.
- There is not sufficient evidence to warrant rejection of the
claim that the first population mean is not equal to the second
population mean.
- The sample data support the claim that the first population
mean is not equal to the second population mean.
- There is not sufficient sample evidence to support the claim
that the first population mean is not equal to the second
population mean.