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  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 values:4.1,4.8,5.0,3.7,4.2,5.4,4.0,4.3

mean = x= sum of terms/number of terms = 35.5/8 = 4.4375

sd = = 0.5731

n = 8 , df = n - 1 = 8 - 1 = 7

t(, N-1) = 2.365

Standard error of the mean = SEM = S/n = 0.5731 /sqrt(8) = 0.2026

  the confidence limits at a 95% CI = x +/- t *SEM

= 4.4375 +/- (2.365* 0.2026 )

= 3.9583 , 4.9166

= (3.96 , 4.92) (rounded)

=> 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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