Question

1. In order to compare the true mean for two populations, μ ₁, and, μ ₂, independent random samples of individuals are selected from each population. Descriptive statistics found for each sample are provided in the table below :

Group Statistics
	GROUP	n	Mean	Std. Deviation
Variable	1 2	9 7	16.09 4.55	0.588 9.438

Independent Samples Test
		Levene's Test for Equality of Variances		t-test for Equality of Means
		F	Sig.	t	df	Sig. (2-tailed)	Mean Difference	Std. Error Difference	95% Confidence Interval of the Difference
									Lower	Upper
Variable	Equal variances assumed Equal variances not assumed	13.80	0.002	3.70 3.23	14 6.04	0.002 0.018	11.54 11.54	3.12 3.57

3. 
   i) Carry out a hypothesis test for a significant difference between the two population means, at significance level α = 0.05.
   The hypotheses being tested are:
   H ₀: μ ₁ - μ ₂ = 0
   H _a: μ ₁ - μ ₂ ≠ 0.
   Complete the test by filling in the following blanks, inputting values as printed in the output:
   An estimate of the difference in population means is  .
   Use the output of Levene's test to determine if the population variances can be assumed to be equal, σ ₁=σ ₂. The p-value is  , there  (is evidence/is no evidence)to suggest that the two population variances are unequal.
   Choosing the correct line of output, the standard error is  .
   The test statistic has value TS=  .
   The pvalue is  .Since the pvalue is  (smaller/larger) than the significance level α, there  (is evidence/is no evidence)to reject the null hypothesis, H ₀ of no difference between the two population means, μ ₁ and μ ₂.
   
   ii) The difference in population means is estimated by a 95% confidence interval, but is missing in the output. Use the information to calculate this interval, giving answers correct to 2 dec places.
   The difference between the population means, the mean of population 1, μ ₁, minus the mean of population 2, μ ₂, is estimated to be between  and  .

Answer 1

using levene test

we reject the null hypothesis

the population variances can not be assumed to be equal

standard error = 3.5728

TS = 3.23

p-value = 0.0178

Since the pvalue is smaller than the significance level α, there is evidence to reject the null hypothesis, H ₀ of no difference between the two population means,

ii)

95% confidence interval

(2.81,20.27)