Question

Sub: Test on Hypothesis (Maths)

Kindly solve the sum and provide the detailed step by step method:-

A random sample of size 15 has 50 as mean, the sum of the squares of the deviation taken from mean is 130.Can this sample be regarded as taken from the population having 53 as mean?. Obtain 95% and 99% confidence limits of the mean for the population.

Answer 1

Given,

Sample Size : n=15

Sample mean : = 50

Sum of squares of the deviation from mean i.e = 130

Sample standard deviation : s

Formula for Confidence Interval for Population mean when population Standard deviation is not known

for 95% confidence level = (100-95)/100 =0.05

/2 = 0.05/2 =0.025

t/2,n-1 =t0.025,14 = 2.1448

95% confidence interval for the mean of the Population

95% confidence limits for the mean of the Population : 48.3125 and 51.6875

As 53 > upper confidence limit : 51.6875; This sample can not be regarded as taken from the population having 53 as mean

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for 99% confidence level = (100-99)/100 =0.01

/2 = 0.01/2 =0.005

t/2,n-1 =t0.005,14 = 2.9768

99% confidence interval for the mean of the Population

99% confidence limits for the mean of the Population : (47.6579,52.3421)

As 53 > upper confidence limit : 52.3421; This sample can not be regarded as taken from the population having 53 as mean