Listening to music has long been thought to enhance intelligence, especially dur

Question

Listening to music has long been thought to enhance intelligence, especially during infancy and childhood. To test whether this is true, a researcher records the number of hours that eight high-performing students listened to music per day for 1 week. The data are listed in the table.

(a) Find the confidence limits at a 95% CI for this one-independent sample. (Round your answers to two decimal places.)

To save money, a local charity organization wants to target its mailing requests for donations to individuals who are most supportive of its cause. They ask a sample of 5 men and 5 women to rate the importance of their cause on a scale from 1 (not important at all) to 7 (very important). The ratings for men were

M1 = 6.3.

The ratings for women were

M2 = 5.3.

If the estimated standard error for the difference

(sM1 M2)

is equal to 0.25, then consider the following.

(a) Find the confidence limits at an 80% CI for these two-independent samples. (Round your answers to two decimal places.)

4.3 4.9 5.0 3.7 4.1 5.4 4.0 4.3

Explanation / Answer

x

4.3

4.9

5

3.7

4.1

5.4

4

4.3

Mean =

4.4625

Standard deviation =

0.57802

Confidence Interval:

Here the sample size is small and the value of standard deviation is unknown we use t-distribution to find the confidence interval.

The formula for confidence interval is as below:

X bar (-/+) E

X bar = sample mean = 4.4625

E = margin of error = tc * (s / Ön)

tc is the critical value, s is the sample standard deviation and n is the sample size.

s = 0.57802

n = 8

Degrees of freedom = n – 1 = 8 – 1 = 7

We need to find critical t value from table at 5% (100% - 95%) level of significance for 7 degrees of freedom.

We get the critical value as 2.365

X bar (-/+) E

4.4652 (-/+) [ 2.365 * (0.57802 / Ö8)]

= 4.4652 (-/+) 0.4833

= 3.98 and 4.95

The 95% confidence interval is 3.98 and 4.95

x

4.3

4.9

5

3.7

4.1

5.4

4

4.3

Mean =

4.4625

Standard deviation =

0.57802

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