Question

Researchers believe that male and female students at UD differ in the population mean number of hours of sleep that each group gets each night. Test this belief at the 10% level of significance with the following data obtained from the Combined Class Dataset, (and let Males be Group #1).
ASSUME THAT σ12=σ22 This question comes out of section 10.2, specifically from p. 475 in the Note and Comment section. WHY?

Female Hrs:	8	7	7	0	10	8	8
Male Hrs:	4.5	6	8	3	6	6	7.5	7	5

Enter your Summary Statistics here (rounded off to the 2^nd decimal place, if necessary):

	Female	Male
X:
s:
n:

      Q9: Write out your Null (H₀) and Alternative Hypotheses (H_A).

       

        H0:

        HA:

    Q10: What kind of a TS will you calculate for this pair of hypotheses?
             Z₀? T₀? F₀? χ02?

    Q11: Calculate the value of the TS you would use to run this hypothesis                 test, complete with degrees of freedom, if necessary.

    Q14: Calculate the PValue for your TS (and if you’re working from one of the          probability tables, you might have a statement like: “0.01< PV <0.05”).

Answer 1

Solution :

If x1's denote the observations of female and x2's be the observations of male then ,

	Female	Male
	6.86	5.89
s	3.18	1.56
n	7	9

Q9)

Since here we want to see that if mean of both male and female hours are same or not So here we will apply t test for 2 independent samples. (two tailed)

Where is the population mean of females hours

and be the population mean of male hours.

Q10)

Here we will t test statistic to see if there is any difference between mean of male and female or not.

Since here population standard deviation is not known.

Q11)

test statistic is given by:

Q14)

Here also we can see that p value = 0.471123 >

P value is lies between 0.02 < p < 0.05

which also implies the same.

that we do not have enough evidence to reject the null hypothesis.

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