Question

You wish to test the following claim ($H_1$) at a significance level of $\alpha = 0.01$. $H_0: \mu_1 = \mu_2$ $H_1: \mu_1 \neq \mu_2$ You obtain a sample of size $n_1 = 12$ with a mean of $\bar{x}_1 = 62.8$ and a standard deviation of $s_1 = 9.9$ from the first population. You obtain a sample of size $n_2 = 6$ with a mean of $\bar{x}_2 = 48.4$ and a standard deviation of $s_2 = 9.4$ from the second population. Find a confidence interval for the difference of the population means. Note: If you do not have a Ti-84 and the degrees of freedom is not on Table F, then please use the T.INV(Area to left, df) function in Google Sheets to find the critical value to 3 decimal places. Round your interval end points to one decimal point. confidence interval = (Use interval notation.) The test statistic is... the confidence interval contains zero all values in the confidence interval are below zero all values in the confidence interval are above zero 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.

          You wish to test the following claim ($H_1$) at a significance level of $\alpha = 0.01$.
$H_0: \mu_1 = \mu_2$
$H_1: \mu_1 \neq \mu_2$
You obtain a sample of size $n_1 = 12$ with a mean of $\bar{x}_1 = 62.8$ and a standard deviation of $s_1 = 9.9$ from
the first population. You obtain a sample of size $n_2 = 6$ with a mean of $\bar{x}_2 = 48.4$ and a standard
deviation of $s_2 = 9.4$ from the second population.
Find a confidence interval for the difference of the population means. Note: If you do not have a Ti-84 and
the degrees of freedom is not on Table F, then please use the T.INV(Area to left, df) function in Google
Sheets to find the critical value to 3 decimal places. Round your interval end points to one decimal point.
confidence interval = 
(Use interval notation.)
The test statistic is...
the confidence interval contains zero
all values in the confidence interval are below zero
all values in the confidence interval are above zero
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.

You wish to test the following claim (H1) at a significance level of α = 0.01.
H0: μ1 = μ2
H1: μ1 ≠μ2
You obtain a sample of size n1 = 12 with a mean of x̅1 = 62.8 and a standard deviation of s1 = 9.9 from
the first population. You obtain a sample of size n2 = 6 with a mean of x̅2 = 48.4 and a standard
deviation of s2 = 9.4 from the second population.
Find a confidence interval for the difference of the population means. Note: If you do not have a Ti-84 and
the degrees of freedom is not on Table F, then please use the T.INV(Area to left, df) function in Google
Sheets to find the critical value to 3 decimal places. Round your interval end points to one decimal point.
confidence interval =
(Use interval notation.)
The test statistic is...
the confidence interval contains zero
all values in the confidence interval are below zero
all values in the confidence interval are above zero
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.

Added by Stephanie E.

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