Question

In order to use a 90% confidence interval to compare admission exam scores for sophomores (group #1) and freshmen (group #2), two independent random samples were selected. The results showed:

1-Sophomores: Sample mean = 85, sample standard deviation = 10, sample size = 50.

2-Freshmen: Sample mean = 78, sample standard deviation = 12, sample size = 72.

For forming a 90% confidence interval for μ 1 − μ 2, the multiplier is __________ .

Group of answer choices

1.645

3

1.96

None of the other choices represent a suitable response.

2.576

Answer 1

According to this question, we are to find the 95% confidence interval for the null

Here we have,

Here,

Test-statistic will be-

qhich is distributed as t with degrees of freedom under null

i.e. ,the test is called Fisher's t-test.

The % confidence interval is then given by--

So, the multiplier is ,i.e. None of the choices represent a suitable response.,but 1.645 is approximately close to computed value of multiplier.