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Answer:
90% confidence interval for the population mean test score is [95.40 , 106.59]
Step-by-step explanation:
We are given that the population mean score for mathematics test is 115. It is known that the population standard deviation of test scores is 17.
Also, a random sample of 25 students take the exam. The mean score for this group is 101.
The, pivotal quantity for 90% confidence interval for the population mean test score is given by;
P.Q. = ~ N(0,1)
where, X bar = sample mean = 101
= population standard deviation
n = sample size = 25
So, 90% confidence interval for the population mean test score, is ;
P(-1.6449 < N(0,1) < 1.6449) = 0.90
P(-1.6449 < < 1.6449) = 0.90
P(-1.6449 * <
< 1.6449 *
) = 0.90
P(X bar - 1.6449 * <
< X bar + 1.6449 *
) = 0.90
90% confidence interval for = [ X bar - 1.6449 *
, X bar + 1.6449 *
]
= [ 101 - 1.6449 * , 10 + 1.6449 *
]
= [95.40 , 106.59]
Therefore, 90% confidence interval for the population mean test score is [95.40 , 106.59] .