Question

From the class survey at the beginning of the semester, students were asked to estimate the number of apps on their cellphones. Using a sample of 10 students they gave the following data: 58, 35, 30, 15, 17, 72, 64, 57, 80, 82.

Mean: 51

Median: 57.5

Range: 67

Standard deviation: 25.04

Using the sample data, predict the 90% confidence interval for the mean number of Apps on students’ phones for all students. Answer as a sentence rounding to the nearest tenth.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 51

sample standard deviation = s = 25.04

sample size = n = 10

Degrees of freedom = df = n - 1 = 9

At 90% confidence level the t is ,

t _/2,df = t_0.05,9 = 1.833

Margin of error = E = t_/2,df * (s /n)

= 1.833 * ( 25.04/ 10)

= 14.51

The 90% confidence interval estimate of the population mean is,

- E < < + E

51 - 14.51 < < 51 + 14.51

36.49 < < 65.51

(36.49 , 65.51)