Question

B: The weights of chicken eggs are normally distributed with a mean of 56 grams and a standard deviation of 4.8 grams. You think this value is low, and collect a dozen eggs with a mean weight of 57.5 grams. Use α=0.05.

Part 1 (2 pts): Write your hypotheses in both symbols and words.

Part 2 (4 pts): Test an appropriate hypothesis "by hand" using an alpha level of 0.05. Assume conditions are met (so don't check them). Be sure to include the correct probability notation and use the editor for all work.

Part 3 (4 pts): Support your test with the corresponding confidence interval, again "by hand". Use the editor to show all steps.

Part 4 (3 pts): Write your final conclusion using the test results and interval results. Include a sentence that states whether the test and interval results agree.

Answer 1

the given data are:-

sample mean () = 57.5

population sd () = 4.8

sample mean (n) = 12

level of significance () = 0.05

1).hypothesis:-

in words:-

The population mean weights of chicken eggs are 56 grams

The population mean weights of chicken eggs are greater than 56 grams

2).here, as the population sd is known we will do 1 sample z test for mean.

test statistic be:-

p value :-

=

[ from standard normal table]

3).z critical value for 95% confidence level, one tailed test be:-

the 95% confidence interval for testing the hypothesis be:-

4).decision from p value:-

p value = 0.1401 >0.05 (alpha)

so, we fail to reject the null hypothesis.

decision based on confidence interval:-

as the hypothesized value , 56 is included in the interval , we fail to reject the null hypothesis.

conclusion:-

we conclude that, there is not sufficient evidence to support the claim that , 'The weights of chicken eggs are low' ,  that is the the weight of chickens are greater than 56 pounds at 0.05 level of significance.

*** if you have any doubt regarding the problem please write it in the comment box.if you are satisfied please give me a LIKE if possible..