<u>The graph shown is the second derivative</u>
⇒ first derivative equals the area between
- the second derivative function from 0 to 2
- the axis
<u>Thus the first derivative f(2) equals</u>
<u>However there is an inital position for the first derivative</u> ⇒ f(0) = 2.5
<u>Therefore we must add the initial position to the first derivative found</u>
<u>f(2) = 8 + 2.5 = 10.5</u>
Hope that helps!
Answer:
The decision rule will be as follows: Reject the null hypothesis if test-statistic < -2.5 or fail to reject the
Now, Our test-statistic was -1.96, which is greater than -2.5. Thus, we will fail to reject the null hypothesis.
Step-by-step explanation:
We are given;
Population mean; μ = 432
Sample mean; x¯ = 426
Sample size; n = 24
Variance; Var = 225
Now, standard deviation from variance is; σ = √Var
Thus, σ = √225
σ = 15
Hypothesis is defined as;
Null hypothesis; H0: μ ≥ 432
Alternative hypothesis: Ha: μ < 432
Formula for the test statistic since sample size is less than 30 is;
t = (x¯ - μ)/(σ/√n)
Plugging in the relevant values;
t = (426 - 432)/(15/√24)
t = -1.96
Now,we are given significance level of 0.01; our DF = n - 1 = 24 - 1 = 23.
From t-table attached, we can see that at DF of 23 and significance value of 0.01, the critical value is 2.5
However, this is a left tailed test as the rejection region is to the left.
Thus, the critical value of a left tailed test is negative. Thus, in this case our critical value will be -2.5.
The decision rule will be as follows: Reject the null hypothesis if test-statistic < -2.5 or fail to reject the
Now, Our test-statistic was -1.96, which is greater than -2.5. Thus, we will fail to reject the null hypothesis.
