Question

A professor wants to estimate how many hours per week students study. A simple random sample of 78 students had a mean of 15.0 hours of studying per week. Construct and interpret a 90% confidence interval for the mean number of hours a student studies per week. Assume the population standard deviation is known to be 2.3 hours per week

Answer 1

Answer:

interval=(15.085,14.9515)

Step-by-step explanation:

Table:

CI                                             Z

85%                                     1.440

90%                                     1.645

95%                                     1.960

In order to find the interval/estimate of hours per week students study we consider the formula given below:

Interval=X±$\frac{Z*S}{\sqrt{n} }$

where:

X is the mean hours

Z is the value from Z distribution table of Confidence Interval

n is the sample size of students

S is the standard deviation

X=15, Z=1.645, S=2.3hours, n=78

Interval=15±$1.645*2.3/\sqrt{78}$

Interval=15±0.0485

interval=(15.085,14.9515)