Question

A study of a local high school tried to determine the mean number of text messages

that each student sent per day. The study surveyed a random sample of 114 students

in the high school and found a mean of 195 messages sent per day with a standard

deviation of 73 messages. Determine a 95% confidence interval for the mean,

rounding all values to the nearest whole number.

Answer 1

Answer:

 182   ≤  x  ≤  208    Confidence Interval

Step-by-step explanation:

Normal Distribution

Sample size     n = 114

Sample mean     X  =  195

Sample standard deviation   σ = 73

Confidence Interval  (CI)  95 %     means   α = 5 %         α/2  = 0,025

Values from Z table for  α/2  = 0,025

Z  = -1,97           Z = 1,97

Confidence Interval:

CI           X  - Zα/2* σ/√n   ≤  x  ≤    X  - Zα/2* σ/√n

σ = 73      and  n = 114

73/√114  =  73/10,677   = 6,84

CI     195   - (1,97)* 6,84    ≤  x  ≤    195 + (1,97)* 6,84

        195  -  13,47   ≤  x  ≤   195  + 13,47

        181,53    ≤  x  ≤    208,47

According to rounding criteria

        182   ≤  x  ≤  208