Answer :
Hypothesis test t(s) = - 1.91. We must reject the null hypothesis H₀ at confidence interval 0.95
What do you mean by Hypothesis test?
Hypothesis test: Hypothesis testing is a form of statistical inference that uses data from a sample to draw conclusions about a population parameter or a population probability distribution. First, a tentative assumption is made about the parameter or distribution. This assumption is called the null hypothesis and is denoted by H₀
Sample with a normal distribution of size <30 and n = 25 independent samples
Consequently, we can use t-student analysis.
H₀ => μ₀= 1503 is the null hypothesis in the first test.
The alternative theory is Ha =>μ₀<1503 (from problem condition)
We must now calculate t(s), where t(s) = [(μ-μ₀)/(s/√n)
μ= sample mean
s = sample standard deviation
Then t(s) is equal to (1440 - 1503) / 165 / √25 =>t(s) = - 63 * 5 / 165
t(s) = - 1.91
We now check the t-student table for t(c) (24 degrees of freedom and = 0,05) and discover that t(c) = - 1.711 ( we must remember symmetry in t-student curve)
Thus, we contrast t(s) with t(c)
t(s) = -1.91 t(c) = -1.711
t(s) is smaller than t(c) then our point is in the rejection zone we reject H₀
Hypothesis test t(s) = - 1.91. We must reject the null hypothesis H₀ at confidence interval 0.95
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