Question

You wish to test the following claim (H1H1) at a significance level of α=0.001α=0.001.

      Ho:μ1=μ2Ho:μ1=μ2
      H1:μ1≠μ2H1:μ1≠μ2

You believe both populations are normally distributed, but you do not know the standard deviations for either. However, you also have no reason to believe the variances of the two populations are not equal. You obtain a sample of size n1=24n1=24 with a mean of M1=85.8M1=85.8 and a standard deviation of SD1=19.3SD1=19.3 from the first population. You obtain a sample of size n2=17n2=17 with a mean of M2=89M2=89 and a standard deviation of SD2=12.3SD2=12.3 from the second population.

What is the critical value for this test? (Report answer accurate to three decimal places.)
critical value = ±±

What is the test statistic for this sample? (Report answer accurate to three decimal places.)
test statistic =

The test statistic is...

• in the critical region
• not in the critical region

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.

how would i put this in a Ti- 84

Answer 1

using excel>addin>phstat>two sample t '

we have

Separate-Variances t Test for the Difference Between Two Means
(assumes unequal population variances)
Data
Hypothesized Difference	0
Level of Significance	0.05
Population 1 Sample
Sample Size	24
Sample Mean	85.8
Sample Standard Deviation	19.3000
Population 2 Sample
Sample Size	17
Sample Mean	89
Sample Standard Deviation	12.3000
Intermediate Calculations
Numerator of Degrees of Freedom	596.3280
Denominator of Degrees of Freedom	15.4232
Total Degrees of Freedom	38.6645
Degrees of Freedom	38
Standard Error	4.9416
Difference in Sample Means	-3.2000
Separate-Variance t Test Statistic	-0.6476
Two-Tail Test
Lower Critical Value	-2.0244
Upper Critical Value	2.0244
p-Value	0.5212
Do not reject the null hypothesis

What is the critical value for this test? (Report answer accurate to three decimal places.)
critical value = ±2.024

What is the test statistic for this sample? (Report answer accurate to three decimal places.)
test statistic =-0.648

The test statistic is...

• not in the critical region

This test statistic leads to a decision to...

• 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.