Answer each of the problems below.
Q1. What is the appropriate critical value for each of the following confidence levels and sample sizes? (Remember that in regard to confidence level this implies two-tails)
(a) Critical z-value for an 96% confidence level for sample of size n= 36:
(b) Critical t-value for a 80% confidence level for sample of size n =20:
Q2. Suppose that the population standard deviation is known. N < 30 and the distribution are normal, what is the correct test to use? z - test or t - test?
Q3. Apple iPhone engineers would like to know the mean time for movie downloads. They calculated the download time for a specific movie by 16 randomly selected iPhones, and the data is shown to the right. Assume all download time is normally distributed
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Download time (seconds) of Apple iPhones
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|
24
|
28
|
27
|
22
|
|
23
|
26
|
26
|
25
|
|
23
|
25
|
22
|
21
|
|
24
|
25
|
24
|
27
|
(a) Determine the mean and standard deviation of this sample data.
(b) Determine the expected margin of error amount in using this sample result to estimate the mean download time for this same movie of all Apple iPhones based upon a 95% desired level of confidence.
(c) Determine the 95% confidence interval for the mean download time all iPhones.
(d) State your final confidence interval result in a sentence that interprets the result within the context of the situation.
Q4. Answer the following:
(a) A cereal company claims that the mean weight of the cereal in its packets is at least 14 oz. Express the null and alternative hypotheses in symbolic form. Use the correct symbol for proportion, mean or standard deviation.
(b) The test statistic in a left-tailed test is z = -2.05. Find the p-value. Compare the p-value with the 0.05 significant levels and state the conclusions about the null hypothesis (reject or fail to reject the null hypothesis)
In multiple choice problems 5 and 6, select the best answer.
Q5. A statistical hypothesis test is used to test a claim. You get -1.87 as the test statistic from the collected sample and a -1.65 as your critical value in a left-tailed test. Which of the following is the correct decision statement for the test?
A. Fail to reject the null hypothesis
B. Claim the null hypothesis is true
C. Reject the null hypothesis
D. Claim the alternative hypothesis is false
Q6. A statistical hypothesis test is used to test a claim. You get a P-value of 0.022 on a test with a significance level of 0.01. Which of the following is the correct decision statement for the test?
A. Fail to reject the null hypothesis
B. Claim the null hypothesis is true
C. Reject the null hypothesis
D. Claim the alternative hypothesis is false
Q7. The proportion of people who write with their left hand is equal to 0.1, but it is claimed that the actual proportion of people who write with their left hand is greater than 0.1. Describe the possibleType I error in this situation.
Q8. The data set to the right refers to the ages (years) of randomly selected race car drivers (based on data reported in USA Today). Use a 0.05 significance level to test the claim that the mean age of all race car drivers is greater than 30 years.
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Race car drivers ages (years)
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|
32
|
32
|
33
|
33
|
41
|
|
29
|
38
|
32
|
33
|
23
|
|
27
|
45
|
52
|
29
|
25
|
(a) Give the null and alternative hypotheses for this situation in mathematical notation.
(b) Based upon a 5% level of significance, determine the critical value(s) associated with this hypothesis test.
(c) Determine the sample's test statistic.
(d) State a final conclusion regarding the results of the hypothesis test. Make sure your statement is tied to the context of the problem (age of race car drivers).
Q9. In a KRC Research poll, 1002 adults were asked if they felt vulnerable to identity theft, and 531 of them said "yes." Use a 0.05 significance level to test the claim that the majority of adults feel vulnerable to identity theft.
(a) List the null and alternative hypotheses for this test.
(b) Determine the value of the sample's test statistic.
(c) Determine the critical value(s).
(d) Determine the P-value.
(e) Write a final interpretive sentence tied to the context for the hypothesis test results.
Q10. Self-reported heights and measured heights of twelve males aged 12 - 16 are shown in the table to the right. At the 1% significance level, is there sufficient evidence to support the claim that there is a difference between the average reported heights and the measured heights of males aged 12 -16? All measurements are in inches. Note: Hypothesis testing method work must be shown for credit on this problem.
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Reported Height
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Measured Height
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|
|
|
69
|
67.9
|
|
|
71
|
69.9
|
|
|
64
|
64.9
|
|
|
71
|
68.3
|
|
|
72
|
70.3
|
|
|
61
|
60.6
|
|
|
65
|
64.5
|
|
|
67
|
67.0
|
|
|
58
|
55.6
|
|
|
65
|
64.2
|
|
|
66
|
65.0
|
|
|
70
|
70.8
|
|
Q11. At the right, give an example of a paired data set (with at least 5 pairs) that demonstrates a strong (but not perfect) negative linear correlation.
12. Give a real life example of two variables that are likely to be negatively correlated. Specifically explain why you believe they are negatively correlated.
13. Suppose some researchers determine that there is a significant strong positive correlation between a student's GPA and the final exam grade in MATH 250 Elements of Statsitics. From this correlation, can we determine that a student's GPA is the cause of a high final exam grade in statistics? Explain your answer.
Use the following situation to answer questions 14 to 18 below:
Refers to the table scores of PSAT and SAT on the right in column (H-178 to I-178) to answer the following questions:
|
PSAT
|
SAT
|
|
183
|
2200
|
|
207
|
2040
|
|
167
|
1890
|
|
206
|
2380
|
|
197
|
2290
|
|
142
|
2070
|
|
193
|
2370
|
|
176
|
1980
|
14. Produce a scatterplot of this paired data at the right.
15. Which of the following best describes the correlation that is demonstrated by the scatterplot (Choose the one best answer.)
A. Weak Positive Correlation
B. Strong Positive Correlation
C. Strong Negative Correlation
D. Weak Negative Correlation
16. Determine the sample's correlation coefficient r and the coefficient of determination r2. Then explain clearly whether or not we should conclude that the correlation in these two variables is statistically significant.
17. Give the equation of the line-of-best-fit (trend line), the slope of this line, and explain what the slope means in the context of this problem.
18. One subject not included in the given table had a PSAT score of 158. Find the best predicted SAT score for this student. Is the result close to the reported value of 2150? Given that the data are from volunteered responses, are the results valid?
Attachment:- Assignment.rar