Question

Use technology and the given confidence level and sample data to find the confidence interval for the population mean muμ. Assume that the population does not exhibit a normal distribution. Weight lost on a diet:Weight lost on a diet: 95 % confidence95% confidence n equals 41n=41 x overbar equals 3.0 kgx=3.0 kg s equals 5.8 kgs=5.8 kg What is the confidence interval for the population mean muμ​? 1.21.2 kgless than

Answer 1

Answer:

a.  μ$_{95%} =$ 3 ± 1.8 = [1.2,4.8]

b. The correct answer is option D. No, because the sample size is large enough.

Explanation:

a. The population mean can be determined using a confidence interval which is made up of a point estimate from a given sample and the calculation error margin. Thus:

μ$_{95%} = x_$±(t*s)/sqrt(n)

where:

μ$_{95%} =$ = is the 95% confidence interval estimate

x_ = mean of the sample = 3

s = standard deviation of the sample = 5.8

n = size of the sample = 41

t = the t statistic for 95% confidence and 40 (n-1) degrees of freedom = 2.021

substituting all the variable, we have:

μ$_{95%} =$ 3 ± (2.021*5.8)/sqrt(41) = 3 ± 1.8 = [1.2,4.8]

b. The correct answer is option D. No, because the sample size is large enough.

Using the the Central Limit Theorem which states that regardless of the distribution shape of the underlying population, a sampling distribution of size which is ≥ 30 is normally distributed.