Question

Salaries of entry-level computer engineers have Normal distribution with unknown mean and variance. Than sample standard deviation of three sample is 20 and sample mean is 50,000. Does this sample provide a significant evidence, at a 10% level of significance, that the average salary of all entry-level computer engineers is less than $80,000? Explain (Hypothesis testing)

Answer 1

i am using minitab to solve the problem.

steps :-

copy the data in minitab and name the column x $1596051930854_blob.png$ stat $1596051930978_blob.png$ basic statistics $1596051930897_blob.png$ 1-sample T $1596051930881_blob.png$ select summarized data from the drop down menu $1596051930866_blob.png$ type 3 in sample size, 50000 in sample mean,20 in standard deviation  $1596051931005_blob.png$tick perform hypothesized test $1596051930882_blob.png$in hypothesized mean type 80000 $1596051930906_blob.png$options $1596051930917_blob.png$ in confidence level type 90 $1596051930883_blob.png$ select alternative hypothesis as mean < hypothesized mean $1596051931066_blob.png$ok$1596051931005_blob.png$ok.

***SOLUTION***

here, we will do 1 sample t test for mean as the population variance is unknown and sample size(n) = 3<30.

hypothesis:-

HOJ = 80000

[ claim ]

H, :μ< 80000

the test statistic (t) = -2598.08

p value = 0.000

decision:-

p value = 0.000< 0.10(alpha)

we reject the null hypothesis. There is enough evidence that the average salary of all entry level computer engineer is less than 80000.

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