A sample of 7 measurements, randomly selected from a normally distributed popula

Question

A sample of 7 measurements, randomly selected from a normally distributed population resulted in a sample mean x = 6.1 and sample standard deviation s = 1.45 Using alpha = 0.01 test the null hypothesis that the mean of the population is 6.6 against the alternative hypothesis that the mean of the population is less than 6.6 by giving the following. (a) the degree of freedom 3.143 (b) the critical t value -3.143 (c) the test statistic -0.91 The final conclusion is A. We can reject the null hypothesis that mu = 6.6. B. There is not sufficient evidence to reject the null hypothesis that mu = 6.6

Explanation / Answer

Solution

H0: µ = µ0 = 6.6   Vs H1: µ < 6.6

Test Statistic: t = (n)(Xbar - µ0)/s, where n = sample size = 7, Xbar = sample average = 6.1 and s = sample standard deviation = 1.45.

So, t = - 0.9123   

Under H0, t ~ tn – 1 i.e., t-distribution with degrees of freedom = 6

Given = 0.01, critical point = lower 1% point [H1 being one-sided less than type] of t-distribution with degrees of freedom = 6 = - 3.143

Since the calculated value of t > critical point, H0 is accepted => there is not sufficient evidence to reject the hypothesis that µ = 6.6.

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