Question

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 obtain the following two samples of data.

Sample #1	Sample #2
28 70.9 54 62.1 46.2 64 48.4 49.5 44.2 52.3 57.3 55.5 76.6 33.7 39.6 67.3 68.6 55.1 51.6 53 62.1 64.5 58.4 76.6 49.1 42.9 41.1 54.8 60.4 73.9 46.2 43.4 43.8 46.2 40.6 46.2 28 41.1 26.2 41.1 30.7 47.3 60 29.4 49.5 44.2 52 43.8 54.8 40.1 37.9	71.9 48.4 66.5 69.9 75.2 51.8 48.4 68 52.6 64.9 54.3 67.5 59 56.3 61.2 61.9 46.5 43.7 53.8 42.6 72.7 62.1 55 72.7 41.2 71.1 55.9 59.7 60.1 56.7 64.6 58.8 54.5 69.9 56.9 42.6 56.3 56.3 72.7 57.4 55.7 50.6 54.3 58 58.4 55.2 51.5 58.8

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 degrees of freedom reported from the technology you are using. (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 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.

If you could please show me how to do this answer on a TI84 PLUS as well please

both of the data samples it wants both samples t statistic and whatnot i don't know how to post a photo but this is copied and pasted

Answer 1

	sample #1		sample #2
x1                     =	50.082	x2                    =	58.419
s1                     =	12.507	s2                    =	8.663
n1                    =	51.000	n2                    =	48.000

standard error se=√(S21/n1+S22/n2)=			2.1519
test stat t =(x1-x2-Δo)/Se=		-3.874

p value : =

0.0001

The p-value is. less than alpha

The sample data support the claim that the first population mean is less than the second population mean.

(if you want from ti-84: press stat-edit: put values in L1,L2 register

then again press stat- tests --0:2-SampTInt )