Question

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=20n1=20 with a mean of ¯x1=53.2x¯1=53.2 and a standard deviation of s1=20.4s1=20.4 from the first population. You obtain a sample of size n2=26n2=26 with a mean of ¯x2=62.8x¯2=62.8 and a standard deviation of s2=10.8s2=10.8 from the second population.

1. What is the test statistic for this sample?
   
   test statistic =  Round to 4 decimal places.
   
2. What is the p-value for this sample?
   
   p-value =   Round to 4 decimal places.
   
3. The p-value is...
   • less than (or equal to) αα
   • greater than αα
   
   
4. This test statistic leads to a decision to...
   • reject the null
   • accept the null
   • fail to reject the null
   
   
5. As such, the final conclusion is that...
   • There is sufficient evidence to warrant rejection of the claim that the first population mean is less than the second population mean.
   • There is not sufficient evidence to warrant rejection of the claim that the first population mean is less than the second population mean.
   • The sample data support the claim that the first population mean is less than the second population mean.
   • There is not sufficient sample evidence to support the claim that the first population mean is less than the second population mean.

Answer 1

using excel>addin>phstat>two sample test

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	20
Sample Mean	53.2
Sample Standard Deviation	20.4000
Population 2 Sample
Sample Size	26
Sample Mean	62.8
Sample Standard Deviation	10.8000
Intermediate Calculations
Numerator of Degrees of Freedom	639.7942
Denominator of Degrees of Freedom	23.5931
Total Degrees of Freedom	27.1179
Degrees of Freedom	27
Standard Error	5.0293
Difference in Sample Means	-9.6000
Separate-Variance t Test Statistic	-1.9088
Lower-Tail Test
Lower Critical Value	-1.7033
p-Value	0.0335
Reject the null hypothesis

1. What is the test statistic for this sample?
   
   test statistic =-1.9088
2. What is the p-value for this sample?
   
   p-value =   0.0335
3. The p-value is...
   • less than (or equal to) αα
4. This test statistic leads to a decision to...
   • reject the null
5. As such, the final conclusion is that...
   • There is not sufficient evidence to warrant rejection of the claim that the first population mean is less than the second population mean