Statistics Help Please

Question

Could someone assist me with this please!!!!

 

Twelve different video games showing substance use were observed and the duration times of game play (in seconds) are listed below. The design of the study justifies the assumption that the sample can be treated as a simple random sample. Use the data to construct a 95% confidence interval estimate of μ, the mean duration of game play.

4045  3885  3857  4027  4310  4805  4656  4024  5005  4829  4328  4324

What is the confidence interval estimate of the population mean μ?

? <μ< ? (Round to one decimal place as needed.)

Answer 1

We first need the mean μ and standard deviation σ.

We also know that since we are testing at significance α=1-0.95 =0.05.

Thus we have:

n = 12

x_bar = Σx_i / n = (4045 + ... + 4324) / 12 = 4341.25

s = √ [Σ(x_i - x_bar)² / (n-1)]
= √{ [(4045 - 4341.25)² + ... + (4324 - 4341.25)²] / 11 }
= 395.87

SE = s/√n = 114.28

t^*_df=11 = 2.20    Using P(t ≤ t^*) = 1-α/2 = 0.975

Thus the confidence interval is

x_bar ± t^* · SE = 4341.25 ± 2.20 · 114.28 = ( 4089.83 , 4592.67 )