Question

The following descriptive statistics are calculated from SPSS. Use them to calculate the test statistic.

Group Statistics
	Gender	N	Mean	Std. Deviation	Std. Error Mean
Memory	Male	14	8.2857	3.81149	1.01866
	Female	14	4.7857	1.31140	.35049

1. What is the calculated test statistic?

a) 1.228

b) 3.017

c) 3.249

d) 5.786

2. What is the correct conclusion?

a) Males are not significantly better than females at memory recall (p<.05)

b) Males are significantly better than females at memory recall (p<.05)

c) Males are not significantly better than females at memory recall (p>.05)

d) Males are significantly better than females at memory recall (p>.05)

3. What is the margin of error for calculating a 98% confidence interval for the difference of means?

a) 1.077

b) 2.215

c) 2.479

d) 2.670

4. What are the lower and upper bounds of the 98% confidence interval to estimate the differences of means?

a) 2.423 and 4.577

b) 1.285 and 5.715

c) 1.021 and 5.979

d) 0.830 and 6.170

Answer 1

1. The formula of calculated test statistics is,

where,

Option c is correct.

2. Correct decision

To take a decision p-value is needed.

To find p-value degrees of freedom is needed.

The formula to find the degrees of freedom is,

Using excel the P-value is tdist(test statistics, df, tail) = tdist(3.249, 16, 1) which is 0.0025

P-value < alpha (0.05), reject the null hypothesis.

Option b is correct for the conclusion.

Males are significantly better than females at memory recall (p<.05)

3. The formula of the margin of error is,

where t is the critical value at 98% confidence level

DF = 16

Using excel the t value is =tinv(0.02,16) gives 2.583

Option d is correct.

4. Confidence interval

The formula of the confidence interval is,

Option d is correct.