What’s the connection between input and output in this question
2 answers:
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Answer:
90% confidence interval for the mean time per week spent listening to the radio is .
Step-by-step explanation:
We are given that a recent survey of 51 students reported that the average amount of time they spent listening to music was 11.5 hours per week, with a sample standard deviation of 9.2 hours.
Firstly, the pivotal quantity for 90% confidence interval for the population mean is given by;
P.Q. = ~
where, = sample average amount of time spent listening to music = 11.5
s = sample standard deviation = 9.2 hours
n = sample of students = 51
= population mean per week spent listening to the radio
<em>Here for constructing 90% confidence interval we have used One-sample t test statistics as we know don't about population standard deviation.</em>
<em />
So, 90% confidence interval for the population mean, is ;
P(-1.676 < < 1.676) = 0.90 {As the critical value of t at 50 degree of
freedom are -1.676 & 1.676 with P = 5%}
P(-1.676 < < 1.676) = 0.90
P( <
<
) = 0.90
P( <
<
) = 0.90
<u><em>90% confidence interval for</em></u> = [
,
]
= [ ,
]
= [9.34 hours , 13.66 hours]
Therefore, 90% confidence interval for the mean time per week spent listening to the radio is [9.34 hours , 13.66 hours].