Question

In: Statistics and Probability

For any Hypothesis Test make sure to state Ho, Ha, Test statistic, p-value, whether you reject...

For any Hypothesis Test make sure to state Ho, Ha, Test statistic, p-value, whether you reject Ho, and your conclusion in the words of the claim.

For any confidence interval make sure that you interpret the interval in context, in addition to using it for inference.

round to the thousandths place

The Ajax Company just bought a new machine that makes boots. In a random sample of forty boots produced by the new machine, they find that the mean weight is 1550 grams with a standard deviation of 210 grams. Their old machine produced boots with a true mean weight of 1450 grams. (Answer all 4 parts)

  1. Find a 95% confidence interval for the true mean weight using the new machine.
  2. Interpret the confidence interval in context.
  3. Find the error bound of the above interval.
  4. Is there evidence that the true mean weight for the new machine is different than that of the old machine?Justify!

Solutions

Expert Solution

sample mean, xbar = 1550
sample standard deviation, s = 210
sample size, n = 40
d+G9egrees of freedom, df = n - 1 = 39

Given CI level is 95%, hence α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025, tc = t(α/2, df) = 2.023

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (1550 - 2.023 * 210/sqrt(40) , 1550 + 2.023 * 210/sqrt(40))
CI = (1482.828 , 1617.172)


we are 95% confident that the true mean weight using the new machine. is between 1482.828 and 1617.172


ME = tc * s/sqrt(n)
ME = 2.023 * 210/sqrt(40)
ME = 67.172

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 1450
Alternative Hypothesis, Ha: μ ≠ 1450


Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (1550 - 1450)/(210/sqrt(40))
t = 3.01

P-value Approach
P-value = 0.0046
As P-value < 0.05, reject the null hypothesis.


There is sufficient evidence to conclude that the true mean weight for the new machine is different than that of the old machine


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