Question

Most dermatologists recommend using sunscreens that have a Sun Protection Factor (SPF) of at least 30. One of the authors wanted to find out whether the SPF of sunscreens used by students at her school exceeds this value on average? To collect data, the author surveyed students in her introductory statistics course and found that in a sample of 52 students the mean SPF was 34.55 and the standard deviation of SPF was 20.12. The data were not strongly skewed.​

Required:

Use the Theory-Based Inference applet to find and report the 95% confidence interval for the parameter of interest.

Answer 1

95% confidence interval = ( 28.9485, 40.1515 )

Explanation:

sample size( n ) = 52

mean value ( x )= 34.55

std ( б ) = 20.12

H0 : u ≤ 30

Ha : u > 30 ( claim )

95% confidence interval for mean SPF level ( df = 51 )

= mean value ±
`(2.0076 + (20.12)/(√(52) ) )`

95% confidence interval = ( 28.9485, 40.1515 )

we cannot reject H0