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An article in the Washington Post on March 16, 1993 stated that nearly 45 percent of all Americans have brown eyes. A random sample of 𝑛=82 C of I students found 30 with brown eyes.
We test

𝐻0:𝑝=.45
𝐻𝑎:𝑝≠.45

(a) What is the 𝑧z-statistic for this test?

(b) What is the P-value of the test?

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Related textbook solutions

Introductory Statistics
OER Edition, 2013
Openstax
ISBN: 9781938168208

Related questions

Use the following scenario for questions 6 – 8. In 2016-17, the average SAT score of the UVA first year class was 1420 out of 1600. An advisor in the statistics department is interested in determining whether statistics majors from that class have higher SAT scores than the average. He tests H,:µ = 1420 against Hạ: µ > 1420, where u is the mean SAT score for statistics majors from the 2016-17 first year class. In a simple random sample of 30 statistics majors, he finds a sample mean SAT score of 1440 with sample standard deviation of 40.

6. What is the value of the test statistic for this significance test?

a. 0.09

b. 0.5

c. 2.73

d. 20

7. From what distribution is this test statistic?

a. N(0, 1)

b. N(1420, 7.30)

c. t distribution with 29 degrees of freedom

d. t distribution with 28 degrees of freedom

8.) The p-value for this test is 0.005. Which of the following is a proper interpretation of this p- value?

a.There is a 0.5% chance that the null hypothesis is true.

b. If the population mean SAT score really is 1420, there's a 0.5% chance that the sample a. mean SAT score from 30 statistics majors would equal 1440.

c.If the population mean SAT score really is 1420, there's a 0.5% chance that the sample mean SAT score from 30 statistics majors would be 1440 or lower.

d. If the population mean SAT score really is 1420, there's a 0.5% chance that the sample mean SAT score from 30 statistics majors would be 1440 or higher.

A data set contains information from a random sample of 120 different female dogs who have bred,
40 of which are labradors, 40 are golden retrievers, and 40 are German shepherds.
The variables are:
• Breed: breed of the dog
• LitterSize: the number of pups in the dog’s most recent litter
The data are contained in the file dogs.sav.


(a) [6 marks] Is there evidence of a difference in the population mean litter sizes for the three
breeds? Be sure to state the null and alternative hypotheses, test statistic, null distribution,
p-value, decision, and an appropriate conclusion in plain language.


(b) [3 marks] If appropriate, perform post-hoc tests to determine which breeds have significantly
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(c) [2 marks] Report the 95% pairwise confidence interval for the mean difference in litter sizes
between golden retrievers and German shepherds. Interpret this interval with a sentence in plain
language.


(d) [3 marks] What are the assumptions of the analysis performed in part (a)? State whether
each assumption is reasonable with reference to appropriate SPSS output.

 

A random sample of soil specimens was taken from a large geographic area. The specimens can be assumed to be independent. The amount of organic matter, as a percent, was determined for each specimen. The data are below:
0.14, 0.32, 1.17, 1.45, 3.5, 5.02, 5.09, 5.22
A soil scientist wants to know whether the population mean percent organic matter is different than 4%. A
significance level of α = 0.05 is chosen.

    1. (a)  State hypotheses appropriate to the research question.
    2. (b)  Graph the data as you see fit. Why did you choose the graph(s) that you did and what does it (do they) tell you?
    3. (c)  Regardless of your conclusion from (b), use the bootstrap to perform a test of the hypotheses you stated in (a). Use B = 8000 resamplings. Compute the p-value, and make a reject or not reject conclusion. Then state the conclusion in the context of the problem. In other words, does it seem the mean organic matter level is different than 4%?
    4. (d)  Regardless of your conclusion from part (b), use a T -test to perform a test of the hypotheses you stated in (a). Compute the p-value, and make a reject or not reject conclusion. Then state the conclusion in the context of the problem. In other words, does it seem the mean organic matter level is different than 4%?. (I recommend doing this part with a hand calculator and statistical tables as practice for exam conditions, but you may check your answers using R if you wish.)
    5. (e)  Compare your answers from parts (c) and (d). Which method do you think is better? Are you surprised at the similarity or dissimilarity? What do you think explains this?

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