Mathematics: Adoctor wants to estimate the mean hdl cholesterol of all 20- to 29-year-old females. the number of subjects needed to estimate the mean hdl cholesterol within 3 points with 99% confidence is 160 subjects. suppose the doctor decides that he could be content with only 90% confidence. assuming s=14.7 based on earlier studies, how would this decrease in confidence affect the sample size required?

The answer is 2 1/4 inch or 2.25 inch per 4 1/2 hours...

Adoctor wants to estimate the mean hdl cholesterol

Ответ:

leandroarguijo

13.01.2022

Mathematics

$n=(\frac{1.64(14.7)}{3})^2 =64.57 \approx 65$

So the answer for this case would be n=65 rounded up to the nearest integer

And the sample size would decrease by 160-65=95 subjects

Step-by-step explanation:

1) Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size

ME represent the margin of error

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

2) Solution to the problem

Since the new Confidence is 0.90 or 90%, the value of $\alpha=0.1$ and $\alpha/2 =0.05$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.05,0,1)".And we see that $z_{\alpha/2}=1.64$