Question

THE GOLDEN COMET IS A HYBRID CHICKEN THAT IS PRIZED FOR ITS HIGH EGG PRODUCTION RATE AND GENTLE DISPOSITION. ACCORDING TO RECENT STUDIES, THE MEAN RATE OF EGG PRODUCTION FOR 1-YEAR-OLD GOLDEN COMETS IS 5.2 EGGS/WEEK.

SARAH HAS 42 1-YEAR-OLD HENS THAT ARE FED EXCLUSIVELY ON NATURAL SCRATCH FEED: INSECTS, SEEDS, AND PLANTS THAT THE HENS OBTAIN AS THEY RANGE FREELY AROUND THE FARM. HER HENS EXHIBIT A MEAN EGG-LAYING RATE OF 6.4 EGGS/WEEK.

SARAH WANTS TO DETERMINE WHETHER THE MEAN LAYING RATE, μ, FOR HER HENS IS HIGHER THAN THE MEAN RATE FOR ALL GOLDEN COMETS. USE A 0.05 SIGNIFICANCE LEVEL TO TEST THE CLAIM THAT THE MEAN IS HIGHER THAN 5.2. ASSUME WE KNOW THAT σ = 1.

Answer 1

Given that, sample size (n) = 42, sample mean = 6.4 Eggs/week and population standard deviation = 1

The null and alternative hypotheses are,

H0 : μ = 5.2 eggs/week

Ha : μ > 5.2 eggs/week (claim)

This hypothesis test is a right-tailed test.

Test statistic is,

=> Test statistic = Z = 7.78

p-value = P(Z > 7.78) = 1 - P(Z < 7.78) = 1 - 1 = 0.000

=> p-value = 0.000

Since, p-value is less than 0.05 significance level, we should reject the null hypothesis (H0).

Conclusion : There is sufficient evidence to support the claim that the mean is higher than 5.2.