Question

#5.       Consider the following hypothesis test for the mean of a normally distributed population: Ho: μ=80. A random sample of size 40 is to be taken. The population standard deviation is 20. Write the rejection rule using critical value method; use α=4%. Please clearly identify the test-statistic (t or z or F etc).(15 points)

Answer 1

Given the following hypothesis test for the mean of a normally distributed population:

Ho: μ=80.

Ha: μ 80.

Based on the hypothesis it will be a two-tailed test.

Critical score:

Given that the sample size is n = 40, and also the distribution is normal hence the critical values for the given hypothesis is calculated by the excel formula for normal distribution which is =NORM.S.INV(1-(0.04/2)), thus the critical values are computed as:

Zc = +/- 2.054

Test statistic:

Based on the given details that the sample is normally distributed and the population standard deviation is known hence the test statistic that will be:

Z- statistic.

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