Applied Science

Topics: Statistical hypothesis testing, Normal distribution, Statistics Pages: 6 (833 words) Published: December 8, 2013
MTH540 Statistics
Final Exam
1. Identify the population and the sample.
Thirty-eight nurses working in the San Francisco area were surveyed concerning their opinions of managed health care. Answer: Population is the thirty-eight nurses working in San Francisco The sample is the area that was surveyed concerning opinions and managed health care. 2. Identify the population and the sample.

A survey of 1420 U.S. undergraduate English majors asked which Shakespearean play was most relevant in the year 2000. Answer: The population is a survey of 1420 U. S. undergraduate English majors The sample is the Shakespearean play that was almost relevant in the year 2000. 3. Make a frequency distribution of the data set using five classes. The data set represents the income (in thousands of dollars) of 20 employees at a small business. 30282639343320392833

26393228313933313332
Answer:
Frequency Distribution Table

Income (in thousands of dollars) Frequency 20
1
26
2
28
3
30
1
31
2
32
2
33
4
34
1
39
4

4. Make a relative frequency histogram using the frequency distribution in problem 3. Answer:

5. The following are the height (in feet) and the number of stories of nine notable buildings in Miami. Use the data to construct a scatter plot. What type of pattern is shown in the scatter plot?

Height (in feet) 764625520510484480450430 410 Number of stories 55 47 51 28 35 40 33 31 40

6. Make a Pareto chart of the data set.

Breed
Labrador
Retriever
Golden
Retriever
German
Shepherd
Dachshund
Beagle
Poodle
Yorkshire
Terrier
Number
Registered
(in thousands)

173

66

58

55

52

46

44

Answer:

7. Use the given claim to state a null and an alternative hypothesis. Identify which hypothesis represents the claim. A. Claim: p < 0.205

H0: p = 0.205 vs H1: p ≠ 0.205

2. Because of the large sample size we can assume normality and use the Z statistic for the hypothesis test

3. The p-value is the probability of observing a sample in bigger disagreement with the null hypothesis H0, than we saw in this case.

4. Since the p-value = 0.205 is greater than the significance level we conclude that H0, the null hypothesis, is plausible. Note that we cannot conclude that the null if true, only that it is plausible.

B. Claim: p > 0.70

H0: p = 0.70 vs H1: p ≠ 0.70

2. Because of the large sample size we can assume normality and use the Z statistic for the hypothesis test

3. The p-value is the probability of observing a sample in bigger disagreement with the null hypothesis H0, than we saw in this case.

Find the test statistic

Z = (p - p0) / Sqrt[p0 * (1-p0) / n]
Z = 0.68 - 0.75 / Sqrt[ 0.7*0.3/100]
Z = -1.5275252

the p-value = P[ Z < -1.53] + P[ Z > 1.53] = 0.063 + 0.063 = 0.126

4. Since the p-value = 0.126 is greater than the significance level we conclude that H0, the null hypothesis, is plausible. Note that we cannot conclude that the null if true, only that it is plausible.

8. Test the claim about the population mean µ with a z-test using the given sample statistics and level of significance a.
A. Claim: µ ≠ 0: a = 0.05. Statistics x = -0.69, s = 2.62, n = 60

B. Claim: µ = 7450: a = 0.05. Statistics x = 7512, s = 243, n = 57

9. Find the critical value(s) for the t-test with the indicated sample size n and level of significance a. A. Right–tailed test, n = 8, a = 0.01
Answer: I did this on the calculator DISTR menu which you can access by pressing [2nd] [VARS]. normalcdf came up then I input (8, 0.01) and my answer came out to be -.496

B. Two-tailed test, n = 12, a = 0.05
Answer: I did this on the calculator DISTR menu which...
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