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.

Music Listening Per
Day (in hours) 4.3, 4.7, 5.0, 3.8, 4.3, 5.4, 4.2, 4.3

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

(b) Suppose the null hypothesis states that students listen to 3.5 hours of music per day. What would the decision be for a two-tailed hypothesis test at a 0.05 level of significance?

Retain the null hypothesis because the value stated in the null hypothesis is within the limits for the 95% CI.

Reject the null hypothesis because the value stated in the null hypothesis is outside the limits for the 95% CI.   

Reject the null hypothesis because the value stated in the null hypothesis is within the limits for the 95% CI.

Retain the null hypothesis because the value stated in the null hypothesis is outside the limits for the 95% CI.

Explanation / Answer

Solution:- Given that  4.3, 4.7, 5.0, 3.8, 4.3, 5.4, 4.2, 4.3

mean = 4.5, S = 0.5071

a) the confidence limits at a 95% CI Standard error of the mean = SEM = S/N = 0.5071/8 =  0.179

t(, N-1) = 2.365

=> X ±   t(, N-1)*S/N

=  4.5 ± 2.365 * 0.179

=  4.5 ± 0.42

= ( 4.08 , 4.92)

= 4.08 to 4.92 hours per day

b) option B. Reject the null hypothesis because the value stated in the null hypothesis is outside the limits for the 95% CI.

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