Answer to Question #175857 in Statistics and Probability for Denisse Bisuña

Question

1.In a gymnasium, a physical exercise has a mean length of 30 minutes with a standard deviation of 6 minutes. A PE major wants to estimate the true mean length of the exercise with maximum error pegged at 0.5, adopting the 95% confidence interval. How many respondents does he need?

2.In a paper presentation, the average algebraic reasoning of Grade 8 students in mathematics camp was observed to be 80 with a standard deviation of 4.2. A researcher wants to replicate the study to estimate the true population mean μ to within 0.5 maximum error. If the 95% level of confidence is adopted, how many respondents are needed?

Answer 1

a)

n = (Z critical value*Standard deviation/Error)²

Given σ = 6, E=0.5 and  = 1.96 (The Z critical value for 95% confidence interval obtained  from Z reference table)

n = (1.96*6/0.5)²  = 553.19

We round the value up to 554

Therefore, he needs 554 respondents

b)

n = (Z critical value*Standard deviation/Error)²

Given σ = 4.2, E=0.5 and  = 1.96 (The Z critical value for 95% confidence interval obtained  from Z reference table)

n = (1.96*4.2/0.5)²  = 271.06

We round the value up to 272

Therefore, 272 respondents are needed