Question

Experience raising New Jersey Red chickens revealed the mean weight of the chickens at

five months is 4.35 pounds. The weights follow the normal distribution. In an effort to increase
their weight, a special additive is added to the chicken feed. The subsequent
weights of a sample of five-month-old chickens were (in pounds):
4.41 4.37 4.33 4.35 4.30 4.39 4.36 4.38 4.40 4.39
At the .01 level, has the special additive increased the mean weight of the chickens? Estimate
the p-value.

Answer 1

p-value = 0.1277

Explanation:

p-value is the probability value tell us how likely it is to get a result like this if the Null Hypothesis is true.

Firstly we find the mean and standard deviation of the given data set.

⇒ Mean =
`(4.41 +4.37+ 4.33+ 4.35 +4.30 +4.39 +4.36+ 4.38+ 4.40+ 4.39)/(10)`

⇒ Mean = 4.368

`Standard deviation(\sigma) = \sqrt{(1)/(n)\sum_(i=1)^(n){(x_(i)-\bar{x})^(2)} }`

where,
`\bar{x}` is mean of the distribution.

⇒ Standard Deviation = 0.034

Applying t- test:

Let out hypothesis is:

H₀: μ = 4.35

H₁: μ ≠ 4.35

Now,

Here, μ = Population Mean = 4.35

`\bar{x}`= Sample Mean = 4.368

σ = Standard Deviation = 0.034

n = 10

`t=\frac{\bar{x}-\mu}{(\sigma)/(√(n)) }`

Putting all values we get, t = 1.6777 with (10 -1) = 9 degree of freedom.

Then the p-value at 99% level of significance.

⇒ p-value = 0.1277