Question

Hypothesis Test for Difference in Population Means (σσ Unknown)

You 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. We will assume that the population variances are not equal.

You obtain a sample of size n1=14n1=14 with a mean of M1=78.1M1=78.1 and a standard deviation of SD1=5.6SD1=5.6 from the first population. You obtain a sample of size n2=21n2=21 with a mean of M2=84.7M2=84.7 and a standard deviation of SD2=6.9SD2=6.9from the second population.

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

What is the p-value for this sample? For this calculation, use the conservative under-estimate for the degrees of freedom. The degrees of freedom is the minimum of n₁ - 1 and n₂ - 1. (Report answer accurate to four decimal places.)

p-value =

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.

License

I am strugling to get the p-value for the being it is not equal. I am able to get the correct p-value when it is < or >

Answer 1

x1                     =	78.100	x2                    =	84.700
s1                     =	5.600	s2                    =	6.900
n1                    =	14	n2                    =	21

std error =√(S21/n1+S22/n2)=		2.1230
test stat t =(x1-x2-Δo)/Se =		-3.109

degree of freedom v ='min(n1,n2)-1=

13

p value from excel: : =

tdist(3.109,13,2)=

0.0083

The p-value is less than alpha

This test statistic leads to a decision to reject the null

The sample data support the claim that the first population mean is not equal to the second population mean.