03 27 2014 You take a random sample of 100 students at your university and find that their average GPA is 3 1 If you use this information to help you estimate the average GPA for all students at your university then you are doing what branch of statistics ANS Inferential Statistics You are less likely to be misled by a graph if you Concentrate on the number rather than the form of the graph Random samples of size 81 are taken from an infinite population whose mean and standard deviation are 45 and 9 respectively The mean and standard error of the sampling distribution of the sample mean are 45 and 9 81 Researchers claim that 60 tissues is the average number of tissues a person uses during the course of a cold The company who makes Kleenex brand tissues thinks that fewer of their tissues are needed What are their null and alternative hypotheses H0 60 vs H 1 60 Researchers determined that 60 Kleenex tissues is the average number of tissues used during a cold Suppose a random sample of 100 Kleenex users yielded the following data on the number of tissues used during a cold 52 and s 22 Suppose the test statistic does not fall in the rejection region at 0 05 Which of the following conclusions is correct At 0 05 we do not reject H 0 Researchers determined that 60 Kleenex tissues is the average number of tissues used during a cold Suppose a random sample of 100 Kleenex users yielded the following data on the number of tissues used during a cold 52 and s 22 Suppose the alternative we wanted to test was H1 60 The correct rejection region for 0 05 is reject H 0 if t 1 6604 Researchers determine that 60 Kleenex tissues is the average number of tissues used during a cold Suppose a random sample of 100 Kleenex users yielded the following data on the number of tissues used during a cold 52 and s 22 Using the sample information provided the value of the test statistic is t 52 60 22 10 The line chart below shows pepper prices per pound for each month from January month 1 to December last year By looking at this chart you can see the lowest pepper prices occurred in JULY Observations that are measured at the same time are called data Cross sectional Cross sectional data TIME series Observations that are taken during successive points in time are called Time series data are often graphically depicted on a n which is a plot of the variable of interest over time LINE CHART A n is created by plotting the value of the variable on the vertical axis and the time periods on the horizontal axis LINE CHART A line chart is created by plotting the value of the variable on the axis and the time periods on the axis VERTICAL HORIZONTAL Y X For what type of data are frequencies the only calculations that can be done ANS Nominal Data 2 1 For which type of data are the values arbitrary numbers ANS Nominal Data 2 1 For a two tail test the null hypothesis will be rejected at the 0 05 level of significance if the value of the standardized test statistic z is smaller than 1 96 or greater than 1 96 For a given level of significance if the sample size increases the probability of a Type II error will decrease For testing the difference between two population proportions the pooled proportion estimate should be used to compute the value of the test statistic when the null hypothesis states that the two population proportions are equal For a given sample size n if the level of significance is decreased the power of the test will decrease For a given level of significance if the sample size n is increased the probability of a Type II error will Decrease For statistical inference about the mean of a single population when the population standard deviation is unknown the degrees for freedom for the t distribution equal n 1 because we lose one degree of freedom by using the sample mean as an estimate of the population mean For a 99 confidence interval of the population mean based on a sample of n 25 with s 0 05 the critical value of t is 2 7969 From a sample of 400 items 14 are found to be defective The point estimate of the population proportion defective will be 0 035 Bayes Law is used to compute posterior probabilities Big Rapids local police department must write on average 6 tickets a day to keep department revenues at budgeted levels Suppose the number of tickets written per day follows a Poisson distribution with a mean of 6 5 tickets per day Interpret the value of the mean The expected number of tickets written would be 6 5 per day Bob took a math test whose mean was 70 and standard deviation was 5 The total points possible was 100 Bob s results were reported to be at the 95th percentile What was Bob s actual exam score rounded to the nearest whole number 78 Bob took a statistics test whose mean was 80 and standard deviation was 5 The total points possible was 100 Bob s score was 2 standard deviations below the mean What was Bob s score rounded to the nearest whole number 70 Bob took a biology exam whose mean was 70 with standard deviation 5 He also took a chemistry exam whose mean was 80 with standard deviation 10 He scored 85 on both exams On which exam did he do better compared to the other students who took the exam He did better on the biology exam comparatively speaking Based on sample data the 90 confidence interval limits for the population mean are LCL 170 86 and UCL 195 42 If the 10 level of significance were used in testing the hypotheses H0 201 vs H1 201 the null hypothesis would be rejected Compare the spread of the two histograms below Which of the following is true ANS Data set A has a smaller spread than B Compare the two histograms below Which statement is true ANS The center of Hist A is lower than the center of Hist B use the scale of the x axis Compare the two histograms below Which statement is true ANS The spreads of both histograms are the same Compare the two histograms below Which statement is true ANS The shapes of Both are the same Car buyers were asked to indicate the car dealer they believed offered the best overall service The four choices were Carriage Motors C Marco Chrysler M Triangle Auto T and University Chevrolet U The following data were obtained What percentage of car buyers identified Carriage Motors as having the best overall service ANS 14 40 35 or 35 Chebysheff s Theorem states that the percentage of measurements in a data set that fall within three standard deviations of their mean is at least 89 Assuming a linear relationship between X and Y if …