Question

The Basic Steps to Calculating a Hypothesis Test

You want to start by determining whether you are interested in working with a mean or a proportion. Then identify each of the parts listed below.

1. In order to use the formulas for a hypothesis test we first need to confirm that the sample size requirements for the central limit theorem are satisfied. See the notes for more information. If the sample size is not met acknowledge that you need to proceed with caution.
2. Identify the null and alternative hypotheses. The null hypothesis will be listed first. When working with a proportion the hypothesis will include that symbol for the population proportion, p. When working with a mean the hypothesis will include that symbol for the population mean, µ.
3. Calculate the appropriate test statistic. When working with proportions you will calculate a z-statistic. When working with means you will calculate a t-statistic.
4. Compare your test statistic to the appropriate distribution to find the p-value.
5. Conclude the test in context of the problem.

For each of the four problems below provide all of the steps listed above. Complete all of the work by hand and show your work. You may use the applications listed in the notes to check your work.

4. Chips Ahoy cookies claim that there are more 1,000 chips in every bag. A group of Air Force cadets bought bags of Chips Ahoy! cookies from all over the country to verify the claim . They hand counted the number of chips in 42 bags. They found x=1261.6 chips and s = 117.6 chips. Use α = 0.01.

Answer 1

Hypothesis : Vs  

Since , the population standard deviation is not known.

Therefore , use t-distribution.

Now , df =degrees of freedom=n-1=42-1=41

The test statistic is ,

The p-value is ,

p-value = ; The excel function is , =TDIST(14.4163,41,1)

Decision : Here , p-value <

Theerfore , reject the null hypothesis.

Conclusion : Hence , there is sufficient evidence to support the claim that there are more 1,000 chips in every bag.