For each statement, select the correct null hypothesis, H0H0, and alternative hypothesis, HaHa, in symbolic form. (a) The mean height of all adult American males is 69 inches (5 ft 9 in). A researcher wonders if young American males between the ages of 18 and 21 tend to be taller than 69 inches. A random sample of 100 young American males ages 18 to 21 yielded a sample mean of 71 inches. A. H0:x¯≥71 , Ha:x¯<71 B. H0:x¯≤69 , Ha:x¯>69 C. H0:μ≤69 , Ha:μ>69 D. H0:μ≥71 , Ha:μ<71 E. H0:μ>69 , Ha:μ<69 F. H0:μ=69 , Ha:μ≠69 (b) A certain type of hummingbird is known to have an average weight of 4.55 grams. A researcher wonders if hummingbirds (of this same type) living in the Grand Canyon differ in weight from the population as a whole. The researcher finds a sample of 30 such hummingbirds from the Grand Canyon and calculates their average weight to be 3.75 grams. A. H0:μ<4.55 , Ha:μ=4.55 B. H0:μ=3.75 , Ha:μ≠3.75 C. H0:μ≥4.55 , Ha:μ<4.55 D. H0:x¯≤3.75 , Ha:x¯>3.75 E. H0:x¯≥4.55 , Ha:x¯<4.55 F. H0:μ=4.55 , Ha:μ≠4.55 (c) According to the Merck Veterinary Manual, the average resting heart rate for a certain type of sheep dog is 115 beats per minute (bpm). A Montana farmer notices his aging sheep dog has been acting more lethargic than usual and wonders if her heart rate is slowing. He measures her heart rate on 15 occasions and finds a sample mean heart rate of 118.2 bpm. A. H0:x¯=118.2 , Ha:x¯≠118.2 B. H0:x¯≤115 , Ha:x¯>115 C. H0:μ≤115 , Ha:μ>115 D. H0:μ=115 , Ha:μ≠115 E. H0:μ≥115 , Ha:μ<115 F. H0:μ≥118.2 , Ha:μ<118.2
For each statement, select the correct null hypothesis, H0H0, and alternative hypothesis, HaHa, in symbolic form.
(a) The mean height of all adult American males is 69 inches (5 ft 9 in). A researcher wonders if young American males between the ages of 18 and 21 tend to be taller than 69 inches. A random sample of 100 young American males ages 18 to 21 yielded a sample mean of 71 inches.
A. H0:x¯≥71 , Ha:x¯<71
B. H0:x¯≤69 , Ha:x¯>69
C. H0:μ≤69 , Ha:μ>69
D. H0:μ≥71 , Ha:μ<71
E. H0:μ>69 , Ha:μ<69
F. H0:μ=69 , Ha:μ≠69
(b) A certain type of hummingbird is known to have an average weight of 4.55 grams. A researcher wonders if hummingbirds (of this same type) living in the Grand Canyon differ in weight from the population as a whole. The researcher finds a sample of 30 such hummingbirds from the Grand Canyon and calculates their average weight to be 3.75 grams.
A. H0:μ<4.55 , Ha:μ=4.55
B. H0:μ=3.75 , Ha:μ≠3.75
C. H0:μ≥4.55 , Ha:μ<4.55
D. H0:x¯≤3.75 , Ha:x¯>3.75
E. H0:x¯≥4.55 , Ha:x¯<4.55
F. H0:μ=4.55 , Ha:μ≠4.55
(c) According to the Merck Veterinary Manual, the average resting heart rate for a certain type of sheep dog is 115 beats per minute (bpm). A Montana farmer notices his aging sheep dog has been acting more lethargic than usual and wonders if her heart rate is slowing. He measures her heart rate on 15 occasions and finds a sample mean heart rate of 118.2 bpm.
A. H0:x¯=118.2 , Ha:x¯≠118.2
B. H0:x¯≤115 , Ha:x¯>115
C. H0:μ≤115 , Ha:μ>115
D. H0:μ=115 , Ha:μ≠115
E. H0:μ≥115 , Ha:μ<115
F. H0:μ≥118.2 , Ha:μ<118.2
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