Question

The director of the admissions at a large university advises parents of incoming students about the cost of textbooks during a typical semester. He selected a sample of 100 students and recorded their textbook expenses for the semester. He then computed a sample mean cost of $315.40 and a sample standard deviation of $43.20

Required:
Using the 0.10 level of significance, is there evidence that the population mean is above $300?

Answer 1

The calculated value t = 3.5648> 1.9842 at 0.1 level of significance

The null hypothesis is rejected

The mean of the sample does not come from the Population

Explanation:

Step(i):-

Given that sample size 'n' = 100

Mean of the sample x⁻ = 315.40

The standard deviation of the sample (s) = 43.20

Level of significance = 0.1

Mean of the Population = 300

Null hypothesis: H₀: x₀ = μ

Alternative Hypothesis: H₁: x₀ ≠ μ

Step(ii):-

Test statistic

`t = (x^(-)-mean )/((S)/(√(n) ) )`

`t = (315.40-300 )/((43.20)/(√(100) ) )`

t = 3.5648

Degrees of freedom = n-1 = 100-1 =99

`t_{(0.1)/(2) , 99} = t_(0.05,99) = 1.9842`

The calculated value t = 3.5648> 1.9842 at 0.1 level of significance

The null hypothesis is rejected

The mean of the sample does not come from the Population