The weights of four randomly chosen bags of horse carrots, each bag labeled 20 pounds. Assume that the distribution of weights is Normal. The 95% confidence interval for the mean weight of all bags of horse carrots was (19.55, 21.00). Does the interval provide sufficient evidence to reject the null hypothesis that the population mean weight is 20 pounds at 0.05 significance level? why?

Step-by-step explanation:

Hello!

A random sample of 4 bags of horse carrots was taken and weight. Each bag is labeled with weight= 20 pounds.

The study variable is X: the weight of a horse carrot bag. This variable has a normal distribution.

Using the sample information a 95% CI was constructed: [19.55;21.00]pounds to estimate the mean weight of the carrot bags.

Using this confidence interval you have to decide whether or not to reject the hypothesis that the mean weight is 20 pounds, symbolically:

H₀: μ = 20

H₁: μ ≠ 20

α: 0.05

To decide over statistical hypothesis using a confidence interval several conditions should be met:

1) The hypothesis and the confidence interval should be for the same population parameter.

2) The hypothesis should be two-tailed (= vs. ≠)

3) The Confidence level and the Significance level should be complementary (If 1 - α= 0.95 then α=0.05)

All three conditions are met, then the decision rule is:

If the CI includes the value for the parameter stated in the null hypothesis, you do not reject the null hypothesis.

If the CI doesn't include the value for the parameter stated in the null hypothesis, you reject the null hypothesis.

20 is included in the given CI, then the decision is to not reject the null hypothesis.

You can conclude at 5%, that the average weight of horse carrot bags is 20 pounds.

I hope this helps!

step-by-step explanation: