State the null hypothesis H0 and the alternative hypothesis

State the null hypothesis H₀ and the alternative hypothesis H_a that would be used for a hypothesis test for each of the following statements.

(a) The mean age of the youths who hang out at the mall is less than 16 years. (choose right answer)

H₀: < 16 yrs vs. H_a: < 16 yrs

H₀: = 16 yrs () vs. H_a: > 16 yrs

  H₀: > 16 yrs vs. H_a: > 16 yrs

H₀: = 16 yrs () vs. H_a: < 16 yrs

(b) The mean height of professional basketball players is greater than 6\'6\".

H₀: = 6 ft 6 in () vs. H_a: < 6 ft 6 in

H₀: > 6 ft 6 in vs. H_a: < 6 ft 6 in    

H₀: < 6 ft 6 in vs. H_a: > 6 ft 6 in

H₀: = 6 ft 6 in () vs. H_a: > 6 ft 6 in

(c) The mean elevation drop for ski trails at eastern ski centers is at least 285 feet.

H₀: < 285 ft vs. H_a: > 285

H₀: > 285 ft vs. H_a: < 285

   H₀: = 285 ft () vs. H_a: < 285

H₀: = 285 ft () vs. H_a: > 285

(d) The mean diameter of the rivets is no more than 0.375 inches.

H₀: > 0.375 in vs. H_a: < 0.375 in

H₀: = 0.375 in () vs. H_a: > 0.375 in

  H₀: = 0.375 in () vs. H_a: < 0.375 in

H₀: < 0.375 in vs. H_a: > 0.375 in

(e) The mean cholesterol level of male college students is different from 200 mg/dL.

H₀: 200 mg/dL vs. H_a: = 200 mg/dL

H₀: = 200 mg/dL () vs. H_a: < 200 mg/dL   

H₀: = 200 mg/dL () vs. H_a: > 200 mg/dL

H₀: = 200 mg/dL vs. H_a: 200 mg/dL

Solution

(a)

Since we are interested to test whether mean age is less or not 4th option is appropriate i.e.

H₀: = 16 yrs () vs. H_a: < 16 yrs

(b)

H₀: = 6 ft 6 in () vs. H_a: > 6 ft 6 in

(c)

H₀: = 0.375 in () vs. H_a: < 0.375 in

(d)

H₀: = 200 mg/dL vs. H_a: 200 mg/dL