Question

According to a study, children ranging from ages 8 to 18 averaged 7.9 hours per day using electronic media. Assume the population standard deviation is 2.2 hours per day. A random sample of 45 children from this age group was selected, with a sample average of 8.7 hours of electronic media use per day. Complete parts a and b below a. Is there support for the claim of the study using the criteria that the sample average of 8.7 hours falls within the symmetrical interval that includes 95% of the sample means if the true population mean is 7.9 hours? Select the correct choice below and fill in the answer box within your choice. (Type an integer or decimal rounded to four decimal places as needed.) The probability P (x2 87)-| symmetrical interval, supporting the claim of the study A . This indicates that the sample average of 8.7 hours falls within the 95% O B. bability P (x2 8 7) . This indicates that the sample average of 8.7 hours falls outside the 95% symmetrical interval, contradicting -te claim of the study b. Identify the symmetrical interval that includes 95% of the sample means if the true population mean is 7 9 hours of electronic media use per day (Type integers or decimals rounded to two decimal places as needed)

Answer 1

here,

a) P(X >= 8.7) = P(Z >= (8.7 - 7.9) / (2.2/sqrt(45))) = P(Z > 2.4393) = 0.0073

option - B is correct

b) for 95% of CI, Z = 1.96

CI = 7.9 +/- 1.96*2.2/sqrt(45)

= 7.9 +/- 0.64

= (7.26 , 8.54)