Question

A sociologist believes that for people under the age of 30, women sleep longer per night on the weekend than men. 16 people were surveyed. Test at alpha =5%. The following summary statistics were determined from the sample.

Men:

Mean hrs = 10.45

SD hrs = 0.95

n=9

Women:

Mean hrs = 11.18

SD hrs = 1.81

n=7

a) State the Null and Alternate Hypothesis in symbols and in words.

b) Calculate the expected results for the hypothesis test sampling distribution, assuming the Null Hypothesis is true. (i.e., name and graph of the sampling distribution, mean and standard error)

c) Identify the standard distribution that best approximates the sampling distribution.

d) Formulate the decision rule(you can use either critical test scores or p-values)

e) Determine the statistical sample results, i.e., the differences between the sample means, the pooled standard deviations, the standard error, the test statistic and p-value.

f) Determine the conclusion in terms of the Null and Alternate Hypotheses. Do the sample results indicate that the sociologist’s claim is supported at alpha= 5%?

Answer 1

a)

1 = men

2 = women

Ho: mu1 = mu2

Ha mu1 < mu2

b)

c)

t-distribution

t= (Xbar1 - Xbar2)/ sqrt((sp^2* (1/n1+ 1/n2) ))

d)

reject if p-value < 0.05

e)

Two-Sample T-Test and CI

Sample N    Mean StDev SE Mean
1       9 10.450 0.950     0.32
2       7   11.18   1.81     0.68

Difference = ? (1) - ? (2)
Estimate for difference: -0.730
95% upper bound for difference: 0.500
T-Test of difference = 0 (vs <): T-Value = -1.05 P-Value = 0.157 DF = 14
Both use Pooled StDev = 1.3856

f)

we fail to reject the null as p-value > 0.05

no, the sample results does not indicate that the sociologist’s claim is supported at alpha= 5%