Inference In Practice A Population Mean And Confidence Intervals

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Inference in practice; Inference about a Population Mean; confidence intervals; The one-sample t confidence interval

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True/False 1. If you were doing a two-tailed test of significance, you would need to divide the α by two, in order to determine the critical region. 2. In order to determine the y-intercept in a regression problem, both the dependent variable and the independent variable must be quantitative. 3. In a random sample of 48 observations from a normal distribution, there will be approximately 12 observations less than the 25th percentile. 4. In a one-tailed test where n=21, the value of the Z-test statistic equals -1.812. If α were set at 0.01, this test would be considered significant 5. If a person had a z-score of 0.50, then their actual raw score has to be above the median. 6. If a statistical test is significant at the 10% (alpha = 0.10) level, then it may or may not be significant at the 5% (alpha = 0.05) level. 7. A correlation coefficient estimated to be close to +1.0 , would be considered to be a very strong linear relationship. 8. If a 99% CI for the population mean age is calculated to be [36yrs, 46yrs]; then this implies that approximately 1% of the population will be older than 46 years old. 9. A test of H0 : μ = 50 against H1 : μ < 50 has test statistic t = -2.35, for n=21. This test would be considered statistically significant at α = 0.01. 10. In estimating the true population mean, if you decrease the level of confidence (say 99% to 90%), then the widthe of the CI would also decrease. FILL IN THE BLANK (Q11- Q20) WITH A NUMBER, A WORD OR A SHORT ANSWER 11. Using the Z-table, find the value of Z such that P( Z < _ ) = 0.95 --------------------------------------------------------------------------------------------------------------------------------12. Complete the following sentence. The P-value of a test is the probability of 13. In performing a two-tailed test for n= 18, the t-test statistic equals 2.10. If alpha = .05, what are the two critical values from the t-table that would define the acceptance and rejection regions? -------------------------------------------------------------------------------------------------------------------------------------14. In a distribution, the mean = 158, the mode = 155 and the median = 152 and the standard deviation =12. Which way is the distribution skewed? . Why? 15. Suppose age was normally distributed in a population with the mean = 62 and variance = 25. A person whose age is 66 would have a z-score of . ------------------------------------------------------------------------------------------------------------------------------------------ 16. A random sample of part-time workers and the length of time (days) that they worked were recorded. The following stem plot has a stem width of 5. (a) ) Calculate the sample standard deviation (b) are there any outliers? If so, what are they? 5| 5| 6| 6| 7| 7| 8| 8| 9| 0 5 2 5 4 8 2 5 2 9 4 9 2 5 0 4 9 3 4 5 0 9| 8 9 -----------------------------------------------------------------------------------------------------------------------------------------17. In recent years there has been a lot of discussion in the medical literature regarding the role of diet in the development of heart disease. Suppose a sample of 18 individuals who eat primarily a vegetarian diet is randomly taken. Their mean cholesterol is found to be 180 mg/dl. Suppose in the general population, the mean cholesterol is 205 mg/dl with a SD of 20mg/dl. Based on the sample data can you want to conclude that the mean cholesterol for vegetarians is less than that of the general population? 17a. What are the null and alternative hypotheses? (Do not do the test) Ho: H1: 17b. If you did a 95% CI, what would be the value of the margin of error? --------------------------------------------------------------------------------------------------------------------------------------18. A Gallup Poll found that 16% of adults were addicted to coffee. The 90% CI for the population mean percent was [ .03 , .29 ]. a) In words, write one or two sentences describing what the 95% confidence means. b) If you later found out that the true mean percent was 10% in the population, would this confidence interval support that finding? Why or why not? ---------------------------------------------------------------------------------------------------------------------------------------19. In a study to determine the relationship for postmenopausal women who either received hormone replacement therapy or no therapy and whether or not they developed breast cancer. 19a. How many variables does this problem contain? 19b. Which variable would be considered the response variable? --------------------------------------------------------------------------------------------------------------------------------------20. A 90 % C.I. for the population mean was calculated as [ 30 , 50 ] using the t-distribution for n=15. Based on this interval what is the value of the standard error? ----------------------------------------------------------------------------------------------------------------------------------------Problems Q21 – Q28 require calculations 21. Use Table A (Z-curve), sketch the curve and shade in the area that answers the question. a) What is P ( Z > -1.45) = b) What is the P ( -.81 < z < + .81 ) = 22. Use the t-distribution, sketch the curve and shade in the area that answers the question. a) What is the P ( t > - 2.093 ) = a) What is the P ( t < when n = 20 ) = .95 when n = 16 ----------------------------------------------------------------------------------------------------------------------------------------23. In a study of physical fitness, a random sample college students volunteered to exercise. Their exercise capacity times (in minutes) are given below. Answer the following questions. 36.0 44.0 a) 28.0 38.0 40.0 28.0 35.5 70.0 42.0 68.0 Calculate a 95% CI for the population mean capacity time. b) Before making an inference about the mean exercise time for the population of college students, what other factors might you consider before making the final confidence interval statement? (Show your work) ----------------------------------------------------------------------------------------------------------------------------------24. Results from the National Health and Nutrition Examination Survey showed that for the population of women age 20-74, their mean cholesterol level is 200 mg/dl. If a random sample of 12 women were taken from the population and their sample mean was equal to 185 and standard deviation equal to 14 mg/dl. Calculate the value of the t-test statistic. (Show your work) --------------------------------------------------------------------------------------------------------------------------------------25. Suppose that scores on the mathematics part of the National Assessment of Educational Progress (NAEP) test for eight-grade students follows a normal distribution with sd equal to 92. You want to estimate the true mean score within +/- 12 points with 90% confidence. a) How large must the sample size be? b) Suppose you find out that the most you can sample is only 100 subjects. Now estimate the confidence level you could attain with n=100. Ho: µ = 40, vs. H1: µ ≠ 40, where n = 16, the value of the t-test statistic is t = + 1.88. 26. In testing: Calculate the p-value for this test. 27. For testing the following hypotheses: H 0 : µ = 44 H 1 : µ ≠ 44 For a random sample of 12 individuals, the calculated Z-test statistic was equal to -2.22 a) Calculate the p-value. b) Based on your p-value answer, would this Z-test be considered significant at alpha equal to 0.05? Why or why not? ----------------------------------------------------------------------------------------------------------------------------------28. The measured glucose level one hour after having a sugary drink varies according to the normal distribution with μ = 145 mg/dl and ϭ = 26 mg/dl. a) What is the level (call it L) such that there is probability of only 0.05 that the sample mean glucose level from four tests falls above L? (Hint: this is a Normal Table problem) b) If a sample of 4 glucose tests actually had a mean of 160 mg, what is the probability of getting a sample mean greater than 160 mg? ...
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