MATH SOLVE

3 months ago

Q:
# A simple random sample of 60 is drawn from a normally distributed population, and the mean is found to be 28, with a standard deviation of 5. Which of the following values is within the 95% confidence interval (z-score = 1.96) for the population mean? Remember, the margin of error, ME, can be determined using the formula ME=z*s/square root n. The value of 26, because it’s not greater than 26.7 and less than 29.3. The value of 27, because it’s greater than 26.7 and less than 29.3. The value of 32, because it’s greater than 23 and less than 33. The value of 34, because it’s not greater than 23 and less than 33.

Accepted Solution

A:

The value of 27 is within 95% confidence interval because it is greater than 26.7 and less than 29.3.What is a confidence interval?In statistics, a confidence interval is a range to estimate for unknown terms.The most common level is the 95% confidence interval.It can be calculated byCI = Mean ± margin of error.α = 1 - 0.95 = 0.05α/2 = 0.025z(0.025) = 1.96We need to find the [tex]\frac{\sigma}{\sqrt{n} }[/tex][tex]\frac{5}{\sqrt{60} }[/tex] = 0.645So, [tex]z \times \frac{\sigma}{\sqrt{n} }[/tex] = 1.96 × 0.645 CI =1.26C.I= 28±1.2652Upper limit = 28+1.2652 =29.2625Lower limit =28-1.2652 =26.7348Hence, The value of 27 is within 95% confidence interval because it is greater than 26.7 and less than 29.3.Learn more about confidence intervals;