Statistical Hypothesis Testing and Sampling Techniques, Exams of Statistics

Download Statistical Hypothesis Testing and Sampling Techniques and more Exams Statistics in PDF only on Docsity! FIN 400: STATISTICS QUESTION S AND ANSWERS. 100% VERIFIED.DOWNLOAD TO SCORE A+. 2023. QN 1:The confidence interval and the two-sided hypothesis test are not equivalent for which of the following testing cases. Correct Answer: Test for a population proportion  I want to test vs. using a test of hypothesis. If we concluded that p is .7 when, in fact, the true value of p is not .7, then we have made a___________________. The correct answer: Type I error  Which of the following sampling techniques will not result in a probability sample? Correct answer : quota  The Z value selected for constructing a given confidence interval is also called what? Correct Answer: The Z value is also called the critical value.  Which of the following statements is false? Correct Answer: H0 refers to a specified value of a sample statistic.  In a hypothesis test, the probability of obtaining a value of the test statistic equal to or even more extreme than the value observed, given that the null hypothesis is true, is referred to as what? Correct Answer: The p-value.  If the p-value is greater than alpha in a two-tail test, what conclusion should you draw? Correct Answer: The null hypothesis should not be rejected.  If the p-value is less than alpha in a one-tail test, what conclusion can you draw? Correct Answer: The null hypothesis should be rejected.  What is the region of rejection for a one-tail Z test? Correct Answer: It is found in the tail that supports the alternative hypothesis.  What determines how close the computed sample statistic has come to the hypothesized population parameter? Correct Answer: The test statistic.  The value (1 - α) is called___________. Correct Answer: The confidence coefficient.  If a test of hypothesis has a Type I error probability of 0.01, what does this mean? Your Answer: If the null hypothesis is true, we reject it 1% of the time.  The t test for the difference between the means of two independent samples makes what assumption? Correct Answer: It assumes all of the above.  In testing for differences between the means of two related populations where the variance of the differences is unknown, how many degrees of freedom exist? Correct Answer: n - 1.  In testing for differences between the means of two related populations, what is the null hypothesis? Correct Answer: The population mean difference is equal to 0. I. Consider the following random sample from a normal population: 10, 5, 9, 12, 7, and 5. What is the 95% confidence interval for the population variance? Correct Answer: (3.12, 48.13) II. 25.1 yards plus or minus 4.1 yards III. Estimators are evaluated on all of the following properties EXCEPT Correct Answer: effectiveness IV. The sample mean is an unbiased point estimator of Correct Answer: the population mean. V. Which of the following is not a property of the arithmetic mean? Correct Answer: It is always equal to the population mean. VI. The sampling distribution of the mean is a distribution of Correct Answer: statistics. VII. A two-dimensional plot of the observed data values on the vertical-axis with their corresponding quantile values from a standardized normal distribution on the horizontal- axis is referred to as a Correct answer: normal probability plot. VIII. The length of brook trout caught in a certain Colorado stream has a mean of 14 inches and a standard deviation of 3 inches. The first quartile for the lengths of brook trout would be C) 11.98 inches. IX. Excel's =RAND() function produces random numbers that are uniformly distributed between 0 and 1. The standard deviation of this distribution is approximately Sample size 15 10 Mean 18 20 Variance 1.2 1.5 How many cans of each soda would need to be sampled in order to estimate the difference in the mean caffeine content to within .10 ounces with 90% liability Correct answer: n1=n2=731 XXII. Since tourism is one of the largest industries in the state of Florida, the economy of the state depends heavily on the number of tourists who visit Florida annually and on the mean amount of money tourists spend while they are in the state. Suppose a study is conducted during two consecutive years, say 1992 and 1993, to compare the mean expenditure of tourists in Florida. Random samples of 21 and 31 tourists (a family is treated as one tourist) are selected in 1992 and 1993, respecti ve and the total expenditure in the state is recorded for each. The results are given in the table 1992 1993 x1=1095 x2=1213 s1=973 s2=1015 n1=21 n2=31 Form a 95% confidence interval for . Correct answer: (.418, 2.160) XXIII. All of the following statements are true regarding the use of the t distribution to compare two population means except: Correct answer: The variances of each random sample are unequal XXIV. A study by a corporation revealed that the mean weekly salary for managers in department A was $1,200 with a standard deviation of $100 (sample size = 64) while the mean weekly salary for managers in department B was $1350 and a standard deviation of $150 ( sample size = 81 ) 4. Construct the 95% confidence interval for the difference between the mean salaries for managers. The correct answer: ( -190.8 , -109.2 ) 26. In which of the following circumstances would a statistician use a matched-pair difference experiment? Your answer: b) A tire manufacturing company would like to determine whether a new steel belted radial tire lasts longer than the present model. Eighteen cars were randomly selected and one of each type of tire was installed on the rear wheels of these eighteen cars. The cars were driven until the tires wore out. For each of the eighteen cars, the differences between distances until wear-out were found. 27. Random samples of size and were drawn from populations 1 and 2 respectively. Values of = 20 and were found. A hypothesis test is conducted. The null hypothesis is that the difference in proportions is 0. The alternative hypothesis is that the difference in proportions is greater than 0. The level of significance for this test is 0.05. The test statistic z is : The correct answer: 2.3 28. Suppose you want to compare the mean of a test taken by males versus the mean of the same test for females. The estimate of the difference in means is to be correct to with 5 points with a confidence coefficient of 0.95. If the sample sizes are to be equal, find . From past records, it is known that the range of test scores is 48. The correct answer: 45 29. Two samples each of size 25 are taken from independent populations assumed to be normally distributed with equal variances. The first sample has a mean of 35.5 and standard deviation of 3.0 while the second sample has a mean of 33.0 and standard deviation of 4.0. Based on the data, the p-value for the F test of equal variances will be .166. Based on this p-value, is the assumption of equal variances correct? Correct Answer: The assumption is correct.  On what is the test for the equality of two population variances based? Correct Answer: The ratio of the two sample variances.  In what type of test is the variable of interest the difference between the values of the observations rather than the observations themselves? Correct Answer: A test for the mean difference between two related populations.  When comparing the difference between two population proportions, a pooled estimate of the population proportion can be used for two-tail tests where the null hypothesis assumes that the population proportions are equal. What is the alternative hypothesis? Correct Answer: H1: π1 not equal to π2  For what purpose is the chi-square test used? Correct Answer: To test for equality of proportions.  What test would you use to determine whether a set of observed frequencies differ from their corresponding expected frequencies? Correct Answer: The chi-square test.  When testing for the independence in a contingency table with 3 rows and 4 columns, the degrees of freedom will the test statistic have? Correct Answer: 6  Which is an alternative approach to using the chi-square test for equality of c proportions? Correct Answer: A chi-square test for independence.  What is the procedure called for making comparisons between all pairs of groups? Correct Answer: The Marascuilo procedure.  When using the chi-square test for differences in two proportions with a contingency table that has r rows and c columns, how many degrees of freedom will the test statistic have? Correct Answer: (r - 1)(c - 1).