Question

You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately o = 52.6. You would like to be 90% confident that your estimate is within 2 of the true population mean. How large of a sample size is required? Hint: Video [+] n = Question Help: Message instructor Submit Question

Answer 1

solution:-

given that σ = 52.6 , margin of error E = 2

the value of 90% confidence from z table is 1.645

sample size formula

n = (z*σ/E)^2

=> n = (1.645*52.6/2)^2

=> n = 1872
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solution:-

given data = 96.3,97,99.6,98.8,99.3,98.9,96.7,99.1,99.8,97.4,98.6,97.9,96.6

mean = 98.1538

standard deviation = 1.2286

n = 13

degree of freedom df = n - 1 = 13 - 1 = 12

we look into t table with df and with 99% confidence

critical value t = 3.055

confidence interval formula

=> mean +/- t * standard deviation/sqrt(n)

=> 98.1538 +/- 3.055 * 1.2286/sqrt(13)

=> (97.113 , 99.195)