I need help with this question please! You randomly select 18 adult male athlete
ID: 3181890 • Letter: I
Question
I need help with this question please! You randomly select 18 adult male athletes and measure the resting heart rate of each. The sample mean heart rate is 64 beats per minute, with a sample standard deviation of 2.5 beats per minute. Assuming the heart rates are normally distributed, should you use the normal distribution, the t-distribution, or neither to construct a 90% confidence interval for the population mean heart rate? Explain your reasoning. A soccer ball manufacturer wants to estimate the mean circumference of soccer balls within 0.1 inch. Determine the minimum sample size needed to construct a 99% confidence interval for the population mean. Assume the population standard deviation is 0.25 inch. A college admissions director wishes to estimate the mean age of all students currently enrolled. In a random sample of 30 students, the mean age is found to be 22.9 years. From past studies, the population standard deviation is known to be 1.5 years, and the population is normally distributed. Construct a 98% confidence interval of the population mean age.
Explanation / Answer
(A)
Though population is normally distributed, we should use t-distribution as sample size is less than 30.
(B)
For 99% CI, z-value = 2.58
here ME = 0.1
ME = z*sigma/sqrt(n)
n = ((2.58*0.25)/0.1)^2 = 41.6025
This means n=42, sample size needed.
(C)
For 98% CI, z-value = 2.33
lower limit = 22.9 - 2.33*1.5/sqrt(30) = 22.2619
upper limit = 22.9 + 2.33*1.5/sqrt(30) = 23.5381