Week 7 Extra Credit

State the null and alternative hypotheses for the statistical test described below.

A. Testing to see if there is evidence that the mean of group 1 is not the same as the mean of group 2.

\(\mu\)₁: mean of group 1

\(\mu\)₂: mean of group 2

• Null hypothesis (H₀): \(\mu\)₁ = \(\mu\)₂

• Alternative hypothesis (H₁): \(\mu\)₁ \(\neq\) \(\mu\)₂

B. Testing to see if there is evidence that a proportion is greater than 0.3.

• Null hypothesis (H₀): p = 0.3

• Alternative hypothesis (H₁): p > 0.3

C. Testing to see if there is evidence that a mean is less than 50.

• Null hypothesis (H₀): \(\mu = 50\)

• Alternative hypothesis (H₁): \(\mu \lt 50\)

D. Testing to see if there is evidence that the proportion of people who smoke is greater for males than for females. Let group 1 be the males and let group 2 be the females.

\(p_m\): proportion of males that smoke

\(p_f\): proportion of females that smoke

• Null hypothesis (H₀): \(p_m = p_f\)

• Alternative hypothesis (H₁): \(p_m > p_f\)

E. Testing to see if there is evidence that the percentage of the population who watch the Home Shopping Network is less than 20%

\(p\): proportion of people who watch the Home Shopping Network

• Null hypothesis (H₀): \(p = 0.20\)

• Alternative hypothesis (H₁): \(p < 0.20\)

F. Testing to see if average sales are higher in stores where customers are approached by salespeople than in stores where they aren’t. Let group 1 be the group of stores where customers are approached by salespeople and let group 2 be the group of stores where customers are not approached by salespeople.

\(\mu_1\): average sales of stores where customers are approached by salespeople

\(\mu_2\): average sales of stores where customers are not approached by salespeople

• Null hypothesis (H₀): \(\mu_1 = \mu_2\)

• Alternative hypothesis (H₁): \(\mu_1 > \mu_2\)

G. Testing to see if there is evidence that the mean time spent studying per week is different between first-year students and upper-class students. Let group 1 be the first year students and let group 2 be the upper-class students

\(\mu_1\): mean time spent studying per week by first-year students

\(\mu_2\): mean time spent studying per week by upper-class students

• Null hypothesis (H₀): \(\mu_1 = \mu_2\)

• Alternative hypothesis (H₁): \(\mu_1 \neq \mu_2\)