A researcher wants to determine if a filling machine at a cereal plant fills the boxes well on average or if the machine needs to be replaced. The machine is intended to fill the packages with 28 grams of cereal. He wants to test the machine to see if the average weight of cereal is less than the intended 28 grams. He performs a one sample t test and calculates hisp-value for the test to be 0.027.

a.For which of the following levels of significance would the result be statistically significant at? (choose all the apply)(0.5 point)

1%5%10%

b.If the significance level was 5%, for which of the followingp-values would your result be statistically significant? (choose all the apply)(0.5 point)

0.00670.0430.140.22

Part 2: Hypothesis Testing Procedure

Recall:Complete the Five Steps for conducting an hypothesis test.(2.5 points; 0.5 point each)

a)Determine appropriate [____________] and [__________________] hypotheses.

b)Check [__________] for performing the test and calculate the [______________].

c)Calculate the []under the assumption the [_______________] is true.

d)Determine if the result is[].

e)Report a[]in the[] of the problem.

Part 3: Salmonella Enteritidis in Ice Cream - Hypothesis Testing

Problem Background:A massive multi-state outbreak of food-borne illness was attributed toSalmonella enteritidis.Epidemiologists determined that the source of the illness was ice cream.To determine the level ofSalmonella enteritidisin the ice cream, they sampled nine production runs from the company that produced the ice cream.The researchers would like to use these data to determine whether the average level ofSalmonella enteritidisin the ice cream is greater than 0.3 MPN/g, since such levels are considered very dangerous using a 5% significance level.

Clarify:Before conducting any test, here are a set of questions to ask yourself:(0 points; FYI only)

How many populations are there?OneTwoMore than two

How many variables are there?OneTwo

What is the response variable?

What type of variable is the response?CategoricalQuantitative

What type of parameter would be useful for summarizing this response?

ProportionMean

Hypothesis Test:You can now implement the Five Steps for hypothesis testing.

1.State the Hypotheses:(2 points)

H₀: ___________=___________and H_a: ______________________ ,

where __________represents: ____________________________________________________

Remember:Your hypotheses and parameter definition should always be a statement about thepopulation(s)under study.

2.Checking the Assumptions and Computing the Test Statistic Assumptions:

a.For this scenario, we need to assume the data are a[___________]sample.We also need to assume that the responses come from a[__________________]distributed [___________________].(1.5 point)

b.Is the assumption of normality really that important with a sample of size of 9?

Why?(1 point)...

c.If the sample size were much larger, would this assumption be as important?

Why?(1 point)...