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31.07.2020 •
Mathematics
The Department of Education would like to test the hypothesis that the average debt load of graduating students with a bachelor's degree is equal to $17,600. A random sample of 28 students had an average debt load of $18,800. It is believed that the population standard deviation for student debt load is $4800. The α is set to 0.05. The confidence interval for this hypothesis test would be .
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Ответ:
A 95% confidence interval for the population average debt load of graduating students with a bachelor's degree is [$17,022.05, $20,577.94].
Step-by-step explanation:
We are given that a random sample of 28 students had an average debt load of $18,800. It is believed that the population standard deviation for student debt load is $4800. The α is set to 0.05.
Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;
P.Q. = ~ N(0,1)
where, = sample average debt load = $18,800
= population standard deviation = $4,800
n = sample of students = 28
= population average debt load
Here for constructing a 95% confidence interval we have used a One-sample z-test statistics because we know about population standard deviation.
So, 95% confidence interval for the population mean, is ;
P(-1.96 < N(0,1) < 1.96) = 0.95 {As the critical value of z at 5% level of
significance are -1.96 & 1.96}
P(-1.96 < < 1.96) = 0.95
P( < < ) = 0.95
P( < < ) = 0.95
95% confidence interval for = [ , ]
= [ , ]
= [$17,022.05, $20,577.94]
Therefore, a 95% confidence interval for the population average debt load of graduating students with a bachelor's degree is [$17,022.05, $20,577.94].
Ответ: