Answer:
I am 90% confident that all Americans age 11.273 to 14.727 own a cell phone
Explanation:
Age data: 8,9,10,11,12,13,14,15,16,17,18
From the data above,
Mean is 13 and Standard deviation is 3.162
Number of sample (n) = 11
Degree of freedom = n - 1 = 11 - 1 = 10
Significance level = 1 - confidence level = 1 - 0.9 = 0.1
Use the t-distribution table to obtain the t-value at half the significance level (0.05) and 10 degree of freedom, t-value is 1.812
Confidence interval is given by [mean + (t-value × standard deviation) ÷ √number of sample] and [mean - (t-value × standard deviation) ÷ √number of sample
Confidence interval = 13 + (1.812×3.162)÷√11 = 13+(5.730÷3.317)= 13 + 1.727= 14.727
Confidence interval = 13 - (1.812×3.162)÷√11 = 13 - (5.730÷3.317) = 13 - 1.727 = 11.273
Confidence interval is 11.273 to 14.727. I am 90% confident that Americans age 11.273 to 14.727 own a cell phone
