Answer:
Explanation:
Hello!
n= 34
The null hypothesis is:
H₀: μ = 150
= 1.65
Df= n-1= 34-1= 33
For the three different alternative hypotheses you have to calculate the corresponding p-value. The alternative hypothesis determines the "direction" of the hypothesis test, whether it is one-tailed or two tailed and in which tail you'll find the rejection region.
Remember, the p-value is defined as the probability corresponding to the calculated statistic if possible under the null hypothesis (i.e. the probability of obtaining a value as extreme as the value of the statistic under the null hypothesis).
a)
H₁: μ ≠ 150
The rejection region is two-tailed, meaning that you'll reject the null hypothesis to small values of t and to high values of t, the p-value is also divided in two tails, one negative and one positive:
P(t₃₃≤-1.65) + P(t₃₃≥1.65)= P(t₃₃≤-1.65) + (1 - P(t₃₃≤1.65))= 0.0542 + (1 - 0.9458)= 2*0.0542= 0.1084
p-value= 0.1084
(Check first attachment for graph of the curves and p-value)
b)
H₁: μ > 150
The corresponding rejection region is one-tailed to the right, meaning that you'll reject the null hypothesis to high values of t, you'll find the p-value in the right tail of the distribution too and to calculate it you have to do as follows:
P(t₃₃≥1.65)= (1 - P(t₃₃≤1.65))= 1 - 0.9458= 0.0542
p-value= 0.0542
(See second attachment for graphic)
c)
H₁: μ < 150
This alternative hypothesis determines a rejection region one-tailed to the left, meaning that you'll reject the null hypothesis to small values of t.(see third attachment) The p-value will also be on the left (negative) tail of the distribution:
P(t₃₃≤-1.65)= 0.0542
p-value= 0.0542
I hope this helps!