1. 2.0537 An automobile manufacturer would like to know what proportion of its c

Question

1. 2.0537

An automobile manufacturer would like to know what proportion of its customers are not satisfied with the service provided by the local dealer. The customer relations department will survey a random sample of customers and compute a 96% confidence interval for the proportion who are not satisfied.

(a) Past studies suggest that this proportion will be about 0.17. Find the sample size needed if the margin of the error of the confidence interval is to be about 0.01.

(You will need a critical value accurate to at least 4 decimal places.)

Sample size:

(b) Using the sample size above, when the sample is actually contacted, 21% of the sample say they are not satisfied. What is the margin of the error of the confidence interval?

MoE:

2. A newspaper conducted a statewide survey concerning the 1998 race for state senator. The newspaper took a SRS of

n=1300 registered voters and found that 670 would vote for the Republican candidate. Let p represent the proportion of registered voters in the state who would vote for the Republican candidate.

We test

H 0: p=.50

Ha:p>.50

(a) What is the

z -statistic for this test?

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

3. Matt thinks that he has a special relationship with the number 3. In particular, Matt thinks that he would roll a 3 with a fair 6-sided die more often than you'd expect by chance alone. Suppose

p is the true proportion of the time Matt will roll a 3.

(a) State the null and alternative hypotheses for testing Matt's claim. (Type the symbol "p" for the population proportion, whichever symbols you need of "<", ">", "=", "not =" and express any values as a fraction e.g. p = 1/3)

H0 =

Ha =

(b) Now suppose Matt makes n = 50 rolls, and a 3 comes up 11 times out of the 50 rolls. Determine the P-value of the test:

P-value =

(c) Answer the question: Does this sample provide evidence at the 5 percent level that Matt rolls a 3 more often than you'd expect?

(Type: Yes or No)

Explanation / Answer

As per the Chegg policy, we are advised to do only 1 question at a time so i am attempting the 3rd one.

3. The statistical software output for this problem is:

One sample proportion summary hypothesis test:
p : Proportion of successes
H0 : p = 0.16666667
HA : p > 0.16666667

Hypothesis test results:

Hence,

a) Hypotheses:

Ho: p = 1/6

Ha: p > 1/6

b) P - value = 0.1558

c) No

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