Answer: 1.711, we accept the null hypothesis.
Step-by-step explanation: this is a question under hypothesis testing for some sample mean.
Let H' be the null hypothesis and H1 be the alternative hypothesis.
H': u = 41,500
H1 : u > 41, 500 ( sample mean x = 43,780)
Where u = population mean = 41,500
s = sample standard deviation = 10,520
From the alternative hypothesis, we can see that the sample mean is greater than the population mean hence making the test upper tailed.
Our test statistics will be a t test and that's because sample size is lesser than 30 ( n = 25) and we are given our sample standard deviation.
We need our critical value and test statistics value to make conclusions.
To get the critical value, we make use of the degree of freedom ( n - 1 = 25 - 1 = 24) and the level of significance (5%).
We check the degree of freedom against the level of significance on a t distribution table.
By doing so we have our critical value as 1.711
Let us now get our test statistics.
The t score is calculated as
x - u / (s/√n)
= 43,780 - 41,500/ (10,520/√25)
= 2280/ (10,520/5)
= 2280/ 2104
= 1.084
By comparing our test statistics to the critical value, we can see that test statistics is lesser than the critical value ( 1.084 < 1.711), hence we accept the null hypothesis.
