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##### Elements of Statistics--FHSU Virtual College- Unit 3 Exam Prepatory Problem

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Question;1. Determine the two chi-squared;(?2) critical values for the following confidence levels and sample sizes.;a. 95% and n=36;b. 99% and n=18;2. We are also interested in estimating the population standard deviation (?);for all FHSU students' IQ score. We will assume that IQ scores are at least;approximately normally distributed. Below are the IQ scores of 30 randomly chosen;students from FHSU campus.;135 127 104 139 133 114 110 137 141 118;115 118 121 141 112 134 115 132 132 118;127 116 136 132 117 129 116 109 115 129;Construct a 95% confidence interval estimate of sigma (?), the population;standard deviation.;3. Assume you need to build a confidence interval for a population mean within;some given situation. Naturally, you must determine whether you should use;either the t-distribution or the z-distribution or possibly even neither based;upon the information known/collected in the situation. Thus, based upon the;information provided for each situation below, determine which (t-, z- or;neither) distribution is appropriate. Then if you can use either a t- or z-;distribution, give the associated critical value (critical t- or z- score) from;that distribution to reach the given confidence level.;a. 95% confidence n=40? known population data believed to be normally;distributed;Appropriate distribution;Associated critical value;b. 90% confidence n=31? unknown population data believed to be normally;distributed;Appropriate distribution;Associated critical value;c. 99% confidence n=29? unknown population data believed to be skewed right;Appropriate distribution;Associated critical value;d. 98% confidence n=100? known population data believed to be very skewed;Appropriate distribution;Associated critical value;4. (Multiple Choice) A hypothesis test is used to test a claim. Suppose the;test is left-tailed and the critical value is -2.75. If the collected sample's;test statistic is -2.15, which of the following is the correct decision;statement for the test?;A. Fail to reject the null hypothesis;B. Fail to reject the alternative hypothesis;C. Reject the null hypothesis;D. Reject the alternative hypothesis;5. (Multiple Choice) A hypothesis test is used to test a claim. Suppose the P;value for a hypothesis test is.008, and the significance level is 0.01. Then;which of the following is the correct decision statement for the test?;A. Fail to reject the null hypothesis;B. Fail to reject the alternative hypothesis;C. Reject the null hypothesis;D. Reject the alternative hypothesis;6. (Multiple Choice) Type II error is;A. Rejecting a true null hypothesis;B. Rejecting a false null hypothesis;C. Failing to reject a false null hypothesis;D. Failing to reject a true null hypothesis;7. It is claimed that more than 75% of college students in Kansas take;education loans. Last year 97 out of 120 randomly selected college students;from Kansas reported that they had student loans. Conduct a hypothesis test to;determine if the proportion of students who have student loan is more than 75%;as claimed. Use a 10% significance level.;a. Is the above information sufficient for you to be absolutely certain that;more than 75% of all students of Kansas have education loans? Why or why not?;b. In establishing a statistical hypothesis testing of this situation, give the;required null and alternative hypotheses for such a test, if the claim is that;more than 75% of the Kansas college students have education loans.;H0;H1;c. Based on your answer in part b, should you use a right-tailed, a;left-tailed, or a two-tailed test? Briefly explain how one determines which of;the three possibilities is to be used.;d. Describe the possible Type I error for this situation--make sure to state;the error in terms of the percent of Kansas college students with education;loans.;e. Describe the possible Type II error for this situation--make sure to state;the error in terms of the percent of Kansas college students with education;loans.;f. Determine the appropriate critical value(s) for this situation.;g. Determine/calculate the value of the sample test statistic.;h. Detemine the P-value.;i. Based upon your work above, is there statistically sufficient evidence in;this sample to support that more than 75% of Kansas college students have;education loans? Briefly explain your reasoning.;8. It is claimed that the national average for the price of gasoline is \$3.42;per gallon. Listed below are gas prices from a sample of 32 gas stations from;Kansas. At the 5% significance level, follow the steps below to conduct a;hypothesis test determine if the average price of gasoline in Kansas is;significantly different than the national average of \$3.42.;3.15 3.27 3.14 3.38 3.49 3.12 3.22 3.31;3.58 3.76 3.26 3.59 3.73 3.12 3.62 3.52;3.08 3.28 2.98 3.33 3.48 3.18 3.28 3.28;3.48 3.46 3.48 3.11 3.48 2.88 3.23 3.48;a. Give the null and alternative hypotheses for this test in symbolic form.;H0;H1;b. Determine the value of the test statistic.;c. Determine the appropriate critical value(s).;d Detemine the P-value.;e. Is there sufficient evidence to support the claim that average price of;gasoline in Kansas is significantly different than the national average of;\$3.42.;9. Captoril is a drug to lower systolic blood pressure. When seven randomly;selected subjects were treated with this drug, their systolic pressure reading;(in MM Hg) were measured before and after the drug was taken. Using a 1%;significance level, is there sufficient evidence to support the claim that;Captoril is effective in lowering the systolic blood pressure? Perform an;appropriate hypothesis test showing necessary statistical evidence to support;your final given conclusion.;PreTest PostTest;200 160;175 171;198 177;170 167;193 176;209 183;155 145;10. Multiple Choice;For each of the following data sets, choose the most appropriate response from;the choices below the table.;Data Set #1 Data Set #2;x y x y;7.4 23.9 -1 -4;23.9 75.1 -2 -10;16.6 55.7 2 5;21.8 68.5 3 4;7 22 -3 -19;13.5 48.3 6 -10;20.9 67.7 7 -20;9.7 30.5 -1 -4;10.4 36 0 1;A. A strong positive linear relation exists A. A strong positive linear;relation exists;B. A strong negative linear relation exists B. A strong negative linear;relation exists;C. A curvilinear relation exists C. A nonlinear relation exists;D. No relation exists D. No relation exists;11. Create a paired data set with five data points (i.e., five x-values and;five corresponding y-values) with a strong (but not perfect) positive linear;correlation. Determine the correlation coefficient value for your data.;x y;12. To answer the following, use the list below that contains information on;the age of 12 female staffs in FHSU and their corresponding pulse rate.;Ages Pulse rates;42 98;34 80;49 98;27 63;42 84;18 49;41 80;21 55;21 56;19 53;19 61;30 74;a. Construct a scatterplot for this data set in the region to the right (ages;as the independent variable, and pulse rate as the dependent.);b. Based on the scatterplot, does it look like a linear regression model is;appropriate for this data? Why or why not?;c. Add the line-of-best fit (trend line/linear regression line) to your;scatterplot. Give the equation of the trend line below.;d. Determine the value of the correlation coefficient. Explain what the value;tells you about the data pairs?;e. Does the value of the correlation coefficient tell you there is or is not;statistically significant evidence that a linear correlation exists between the;variables? Explain your position. (HINT: application of table A-6 is needed!);f. What is the predicted pulse rate of a female staff who is 50 years old.;g. What is the predicted age of a female staff whose pulse rate is 64?

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