##### Question

In: Statistics and Probability

# If you wanted to calculate a 90% confidence interval for the difference in average number of...

If you wanted to calculate a 90% confidence interval for the difference in average
number of friendship contacts between primary aged boys and girls and we are
pretending that df=12, what t scores would you use? (assuming equal variances again)
A. ☐+/- 1.356
B. ☐+/- 2.681
C. ☐+/- 1.782
D. ☐+/- 2.179
E. ☐+/- 3.055
9. Suppose you calculated your 90% interval as described above and your lower
confidence limit was
–2.75 and your upper confidence limit was 3.20. What would that mean?
A. ☐It would mean that boys have 2.75 fewer contacts than girls on average
B. ☐It means that girls have 8.95 more contacts on average than boys
C. ☐It means that there may be no difference between the average number of
contacts for boys and girls
D. ☐It means that girls definitely have more contacts than boys
E. ☐It means that girls have 3.20 times more friendship contacts than boys
10. If you were to increase your confidence level to 99%, holding everything else
constant
A. ☐Your interval would be more precise
B. ☐You would be less likely to miss the population value
C. ☐Your interval would be wider
D. ☐You would have less confidence
E. ☐You would have to change your df

## Solutions

##### Expert Solution

Given
Confidence Level = 90%
df = 12       Degrees of Freedom

For 90% Confidence interval
α = (100-90)/100 = 0.10
Degrees of freedom = df = 12
From the t-tables, or Excel function t.inv.2t(α, df)
t = t.inv.2t(0.10, 12)           (We take the positive value for calculations)
t = 1.782

C. ☐+/- 1.782

9)   Confidence interval is (-2.75, 3.20)
Thus, 0 is part of the confidence interval
which implies that there is a possibility that
"there may be no difference between the average number of
contacts for boys and girls"

C.    ☐   It means that there may be no difference between the average number of
contacts for boys and girls

10)   Confidence interval is given by When we increase the confidence level to 99%
the t-score will increase
Thus the value of will increase
This will increase the width of the confidence interval

C.    ☐ Your interval would be wider

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