(1 point) Working backwards, Part I. A 90% confidence interval for a population mean is (70, 76). The population distribution is approximately normal and the population standard deviation is unknown. This confidence interval is based on a simple random sample of 26 observations. Calculate the sample mean, the margin of error, and the sample standard deviation. Use the t distribution in any calculations. Round non-integer results to 4 decimal places.

a) sample mean x⁻ = 73

b) The margin of error (M.E)  = 3

c) Sample standard deviation(σ) = 8.9404

Step-by-step explanation:

Explanation:-

Step(i):-

Given 90% confidence interval for a population mean is (70, 76)

We know that 90% of confidence intervals are determined by

Given sample size n =26

The degrees of freedom ν=n-1 =26-1=25

 …(i)

…(ii)

Adding (i) and (ii) and simplification , we get

Sample mean = 73

Step(ii):-

Substitute x⁻ = 73 in equation(i)

Margin of error = 3

Step(iii):-

The margin of error is determined by

we have margin of error = 3

Given sample size 'n' =26

Cross multiplication , we get

Standard deviation = 8.9404