Question

In a genetics lab, 65 fruit flies were sampled for the amount of time it takes for them to mature into fully grown adult flies. The test showed an average time of 18.5 days for this to happen. If the data follows a normal distribution with a standard deviation of 59 hours, find the 95% confidence interval for the true mean of the dataset. (Hint: Make sure that the unit of measurements are the same for the given parameters)

A) (18.195 days, 18.805 days)

B) (17.902 days, 19.098 days)

C) (63.88 days, 66.12 days)

D) (17.998 days, 19.002 days)

Answer 1

Confidence interval for Population mean is given as below:

Confidence interval = Xbar ± Z*σ/sqrt(n)

From given data, we have

Xbar = 18.5

σ = 2.4583

[Convert hours in day by dividing it by 24]

n = 65

Confidence level = 95%

Critical Z value = 1.96

(by using z-table)

Confidence interval = Xbar ± Z*σ/sqrt(n)

Confidence interval = 18.5 ± 1.96*2.4583/sqrt(65)

Confidence interval = 18.5 ± 0.5976

Lower limit = 18.5 - 0.5976 = 17.902

Upper limit = 18.5 + 0.5976 = 19.098

Confidence interval = (17.902, 19.098)

Answer:

B) (17.902 days, 19.098 days)