Listening to music has long been thought to enhance intelligence, especially dur
ID: 2932598 • Letter: L
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 4.9 4.9 3.9 4.3 5.6 4.0 4.5
(a) Find the confidence limits at a 95% CI for this one-independent sample. (Round your answers to two decimal places.)
BLANK to BLANK 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.
IT WOULD HELP ME VERY MUCH IF THE WORK IS WORKED OUT STEP BY STEP. Thank you very much...
Explanation / Answer
a.
given that,
( 4.3 4.9 4.9 3.9 4.3 5.6 4.0 4.5 )
calculated,
sample mean, x =4.55
standard deviation, s =0.5606
sample size, n =8
level of significance, = 0.05
from standard normal table, two tailed value of |t /2| with n-1 = 7 d.f is 2.365
we use CI = x ± t a/2 * (sd/ Sqrt(n))
where,
x = mean
sd = standard deviation
a = 1 - (confidence level/100)
ta/2 = t-table value
CI = confidence interval
confidence interval = [ 4.55 ± Z a/2 ( 0.5606/ Sqrt ( 8) ]
= [ 4.55-(2.365 * 0.198) , 4.55+(2.365 * 0.198) ]
= [ 4.081 , 5.019 ]
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interpretations:
1) we are 95% sure that the interval [ 4.081 , 5.019 ] contains the true population mean
2) If a large number of samples are collected, and a confidence interval is created
for each sample, 95% of these intervals will contains the true population mean
B.
mean value is 3.5 hours of music per day
Reject the null hypothesis because the value stated in the null hypothesis is outside the limits for the 95% CI.
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