What is measured by the estimated standard error that is used for the independen

Question

What is measured by the estimated standard error that is used for the independent measures t statistic? One sample has n = 15 with SS = 1660, and a second sample has n = 15 with SS = 1700. Find the pooled variance for the two samples. Compute the estimated standard error for the sample mean differences (i.e. for the two groups). If the sample mean difference (i.e. M_1 - M_2) is 8 points, is this enough to indicate a significant difference for a two-tailed test at the .05 level? If the sample mean difference (i.e. M_1 - M_2) is 12 points, is this enough to indicate a significant difference for a two-tailed test at the .05 level? Siegel (1990) found that elderly people who owned dogs were less likely to pay visits to their doctors after upsetting events than were those who did not own pets. Similarly, consider the following hypothetical data. A sample of elderly dog owners is compared to a similar group (in terms of age and health) who do not own dogs. The researcher records the number o0f visits to the doctor during the past year for each person. The data are as follows: Is there a significant difference in the number of doctor visits between dog owners and control subjects? Use a two-tailed test with alpha = .05.

Explanation / Answer

Given that,

n = 15

SS = 1660

n = 15

SS = 1700

Here sample sizes are equal.

For equal sample sizes the pooled variance formula is,

Sp2 = S12 + S22 / 2

where S12 and S22 we can find by using formula,

S12 = SS/n-1

S22 = SS/n-1
S12 = 1660/15-1 = 1660/14 = 118.57

S22 = 1700/15-1 = 1700/14 = 121.43

Therefore pooled variance is,

Sp2 = 118.57+121.43/2 = 120

Standard error for sample mean differences is,

SE = Sp * sqrt(1/n1 + 1/n2)

Sp = sqrt(120) = 10.95

SE = 10.95*sqrt(1/15 + 1/15) = 4

Here we have given that,

M1-M2 = 8

We have to test the hypothesis that,

H0 : mu1 = mu2 Vs H1 : mu1 not= mu2

Assume alpha = 5% = 0.05

The test statistic is,

t = M1-M2 / SE

t = 8/4 = 2

Here we have to find P-value for taking the decision.

P-value we can find by using EXCEL.

syntax :

=TDIST(x,deg_freedom, tails)

where x is test statistic value.

deg_freedom = 30+30-2 =28

tails = 2

P-value = 0.055

P-value > alpha

Accept H0 at 5% level of significance.

Conclusion : There is sufficient evidence to say that two population means are equal.

In the next part we have given M1-M2 = 12

t = 12/4 = 3

P-value = 0.006

P-value < alpha

Reject H0 at 5% level of significance.

COnclusion : There is not sufficient evidence to say that the two population means are equal.

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