Agricultural scientists are testing a new chicken feed to see whether it increases the number of eggs laid. The scientists divided a flock in half and gave half of the chickens the new feed, while the other half were given a regular feed. The eggs laid in a one-year period for a random sample of 10 chickens using the new feed and 10 chickens using the regular feed are recorded. Assume that the population standard deviation of number of eggs laid is 12 eggs per year for both groups and that the number of eggs laid per year is normally distributed. Let the chickens given the new feed be the first sample, and let the chickens given the regular feed be the second sample. The scientists conduct a two-mean hypothesis test at the 0.05 level of significance to test if there is evidence that the new feed increases the number of eggs laid. (a) H0:μ1=μ2; Ha:μ1>μ2, which is a right-tailed test. (b) z≈0.84 , p-value is approximately 0.201   (c) Which of the following are appropriate conclusions for this hypothesis test?  Select all that apply. Select all that apply:   Reject H0.     Fail to reject H0.      There is sufficient evidence at the 0.05 level of significance to conclude that the mean number of eggs laid per year per chicken fed with the new feed is greater than the mean number of eggs laid per year per chicken fed with the regular feed.     There is insufficient evidence at the 0.05 level of significance to conclude that the mean number of eggs laid per year per chicken fed with the new feed is greater than the mean number of eggs laid per year per chicken fed with the regular feed.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...