A student is interested in becoming an actuary. The student knows that becoming an actuary takes a lot of schooling and will have to take out student loans and wants to make sure the starting salary will be higher than $55,000/year. The student takes a random sample of 30 starting salaries for actuaries and finds a p-value of 0.0392. Use α = 0.05.
a. Choose the correct hypotheses.
H0:μ≠55,000 H1:μ=55,000
H0:μ>55,000 H1:μ≤55,000
H0:μ<55,000 H1:μ≥55,000
H0:μ=55,000 H1:μ>55,000
H0:μ=55,000 H1:μ≠55,000
H0:μ=55,000 H1:μ<55,000
b. Should the student pursue an actuary career?
No, since we can reject the null hypothesis
No, since we can reject the claim
Yes, since we can reject the claim
Yes, since we can can reject the null hypothesis

a) The null hypothesis (H0) tries to show that no significant variation exists between variables or that a single variable is no different than its mean. While an alternative Hypothesis (Ha) attempt to prove that a new theory is true rather than the old one. That a variable is significantly different from the mean.

For this case;

Null hypothesis is that the starting salary will be equal to $55,000/year.

H0:μ=55,000

Alternative hypothesis is that the starting salary will be greater than $55,000/year.

H1:μ>55,000

b) Decision Rule;

P-value > significance level --- accept Null hypothesis

P-value < significance level --- reject Null hypothesis

For this case;

P-value = 0.0392

α = 0.05

Since P-value < 0.05, we can reject null hypothesis.

Therefore, we can accept alternative hypothesis which is the starting salary will be greater than $55,000/year, so the student should pursue an actuary career because the starting salary will be greater than $55,000/year.

- Yes, since we can can reject the null hypothesis