Answer: E (c *) = 13.77766
Step-by-step explanation:
the significance level of 0.05 is known
seeks to calculate the sample for the population medis using the hypothesis
H0: µ = 15
H0: µ 15
sample size n = 35
Degrees of freedom df = n-1 = 35-1 = 34
The critical value for z is -1.645
The critical value for t is -1.691
For \ sigma = 3,
Standard error = 3 /√ 35 = 0.5070926
When obtaining the results of the population standard deviation, we will use the z-score to estimate the critical value.
ex = 15-1645 * 0.5070926 = 14.16583
For s = 4.2,
Standard error = 4.2 / √ 35 = 0.7099296
When we do not know what the population standard deviation is, we can use the statistical t to obtain the critical value
c * = 15-1.691 * 0.7099296 = 13.79951
for s = 5.7,
Standard error = 5.7 / √ 3.5 = 0.9634759
c * = 15-1.691 * 0.9634759 = 13.37076
It is obtained that c * is the critical value for the rejection region in this question
P (c * = 14.16583) = 7/20
P (c * = 13.79951) = 6/20
P (c * = 13.37076) = 1-7 / 20-6 / 20
= 7/20
E (c *) = (7/20) * 14,16583 + (6/20) * 13.79951 + (7/20) * 13.37076
Outcome:
E (c *) = 13.77766
