Help on number 4

Question

Given the two independent samples below, conduct a hypothesis test for the desired scenario. Assume all populations are approximately normally distributed.

Sample 1	Sample 2
124	137
28.6	24.9
4.8	5

 

Test the claim:

Given the null and alternative hypotheses below, conduct a hypothesis test for .

Ho:u1=u2

Ha: u1<u2

1. Given the alternative hypothesis, the test is 
2. Select an answer right-tailed two-tailed left-tailed 
3. Determine the test statistic. Round to four decimal places.T=

Find the P-value. Round to 4 decimals.

1. P-value = 
2. Make a decision. 
3. Fail to reject the null hypothesis.
4. Reject the null hypothesis.
5. Write the conclusion. 
6. There is sufficient evidence to support the claim that population mean 1 is less than population mean 2.
7. There is not sufficient evidence to support the claim that population mean 1 is greater than population mean 2.
8. There is sufficient evidence to support the claim that population mean 1 is greater than population mean 2.
9. There is not sufficient evidence to support the claim that population mean 1 is different than population mean 2.
10. There is not sufficient evidence to support the claim that population mean 1 is less than population mean 2.
11. There is sufficient evidence to support the claim that population mean 1 is different than population mean 2.

Answer 1

Hi Morgan,

1.  Left-tailed. Any time your alternative hypothesis is less than, it is left-tailed.
2. Two ways to do this—first way is to use a TI-80s series calculator. Go to STAT-EDIT-input sample 1 values into L1, input sample 2 values into L2. Then, go to STAT-TESTS-2SampTtest—enter “Data,” change alternative to mu1 < mu2, Pool: no; calculate. You will get t-test statistic, p-value, sample means and standard deviations, and degrees of freedom.

Second way is longer, but you may have to use it if you do not have a TI-80s series calculator.

Formula is:

T = (xbar1 -xbar2) - 0 / sqrt[s1²/n1) + (s2²/n2)]

Xbar1= Sample 1 Mean

Xbar2= Sample 2 Mean

S1= Sample 1 standard deviation

S2= Sample 2 standard deviation

N1= Sample 1 Size = 3

N2= Sample 2 Size = 3

You can compute sample means readily enough by just adding the values together and dividing by 3. You may want to use a calculator or software for standard deviations, as they involve differences of squares, which can induce errors. Both sample sizes are 3.

#4&5. P-value can be found in calculator as described above or from statistical software. You can also get it from a t-table but this is less precise—you can only get a range, not an actual p-value that you can round to 4 decimals.

#6. This depends on your p-value. Your problem does not specify an alpha, that is, a rejection cutoff for p-value, but the most common p-value cutoff is 0.05, so I’ll go with it here. If your p-value falls below 0.05, reject H0. If it exceeds 0.05, fail to reject H0. If you reject, there is sufficient evidence that population mean 1 is less than population mean 2. If you fail to reject, there is not sufficient evidence that population mean 1 is less than population mean 2.

I hope this helps.