STAT 2500 Study Guide Final Exam Fall PDF

A Gallup poll to survey the top concerns of Americans was conducted. Suppose that {.math.inline} women and {.math.inline} men were independently and randomly selected, and that {.math.inline} women and {.math.inline} men chose the state of the economy as their biggest concern. Can we conclude that t...

A Gallup poll to survey the top concerns of Americans was conducted. Suppose that {.math.inline} women and {.math.inline} men were independently and randomly selected, and that {.math.inline} women and {.math.inline} men chose the state of the economy as their biggest concern. Can we conclude that the proportion of women ( [*p*~1~]{.math.inline} ), choosing the state of the economy as their biggest concern, exceeds the proportion of men ( [*p*~2~]{.math.inline} )? Use a significance level of [*α* = 0.05]{.math.inline} for the test. a. State the null and alternative hypothesis b. Determine the test statistic. c. Make a conclusion. A manufacturer claims that the calling range (in feet) of its 900-MHz cordless telephone is greater than that of its leading competitor. A sample of {.math.inline} phones from the manufacturer had a mean range of {.math.inline} feet with a standard deviation of {.math.inline} feet. A sample of {.math.inline} similar phones from its competitor had a mean range of {.math.inline} feet with a standard deviation of {.math.inline} feet. Do the results support the manufacturer\'s claim? Let [*μ*~1~]{.math.inline} be the true mean range of the manufacturer\'s cordless telephone and [*μ*~2~]{.math.inline} be the true mean range of the competitor\'s cordless telephone. Use a significance level of [*α* = 0.05]{.math.inline} for the test. Assume that the population variances are equal and that the two populations are normally distributed. d. Compute the test statistic and *p*-value e. State the conclusion of the hypothesis test. A Gallup poll to survey the top concerns of Americans was conducted. Suppose that {.math.inline} women and {.math.inline} men were independently and randomly selected, and that {.math.inline} women and {.math.inline} men chose the state of the economy as their biggest concern. Give a 95% confidence interval for the difference between the proportion of women and men who state that the economy as their biggest concern. Find the critical value for an ANOVA test if [ ∝  = 0.05, *DFE* = 12, *DFT* = 15]{.math.inline} A pharmaceutical company tested three formulations of a pain relief medicine for migraine headache suffers. For the experiment, 30 volunteers were selected and 10 were randomly assigned to one of three drug formulations. What is *the degrees of freedom for error, DFE,* in this study? Consider the following table: ------------------------------------- ---------------------------- ----------------------- -------------------------- ------------------------ \ \ \ \ [SS]{.math.display}\ [df]{.math.display}\ [MS]{.math.display}\ [*F*]{.math.display}\ \ [among treatments]{.math.display}\ \ 12 \ [error]{.math.display}\ [239.5]{.math.display}\ \ \ \ [total]{.math.display}\ [3997.41]{.math.display}\ {.math.display}\ ------------------------------------- ---------------------------- ----------------------- -------------------------- ------------------------ f. Calculate the sum of squares for error (*SSE*). g. Calculate the *degrees of freedom for treatment* (*DFT*) h. Calculate the mean squares of treatment (*MST*) i. Calculate the *F-statistic*. j. Is the test statistic significant at 0.1? 7. A group of paramedics does not believe that the mean numbers of calls received in one shift are the same for the morning, afternoon, and night shifts. To test this claim, they record the number of calls received during each shift for seven days. Number of Calls per Shift --------------------------- ----------- ------- Morning Afternoon Night 2 3 5 3 4 4 2 4 5 4 5 3 3 3 2 1 2 5 3 5 6 a. Calculate the *F-*statistic. b. Based on this evidence, can the paramedics conclude that the mean number of calls are different for the three shifts? Use a 0.01 level of significance. a. There is enough evidence to support the claim that the mean numbers of calls received per shift are different for the morning, afternoon, and night shifts. b. There is not enough evidence to support the claim that the mean numbers of calls received per shift are different for the morning, afternoon, and night shifts. 8. A study of bone density on {.math.inline} random women at a hospital produced the following results. Determine if the correlation coefficient, *r*, is statistically significant at the 0.05 level. --------------------------------- ------------------------ ------------------------ ------------------------ ------------------------ ------------------------ \ \ \ \ \ \ [Age]{.math.display}\ {.math.display}\ {.math.display}\ {.math.display}\ {.math.display}\ {.math.display}\ \ \ \ \ \ \ [Bone Density]{.math.display}\ {.math.display}\ {.math.display}\ {.math.display}\ {.math.display}\ {.math.display}\ --------------------------------- ------------------------ ------------------------ ------------------------ ------------------------ ------------------------ 9. The table below gives the number of parking tickets received in one semester and the GPA for seven randomly selected college students who drive to campus. Using this data, consider the equation of the regression line, [*ŷ* = *b*~0~ + *b*~1~*x*]{.math.inline}, for predicting the GPA of a college student who drives to campus based on the number of parking tickets they receive in one semester. Keep in mind, the correlation coefficient may or may not be statistically significant for the data given. Remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant. -------------------------------------- ------------------------ ------------------------ ------------------------ ------------------------ ---------------------- ------------------------ ------------------------ \ \ \ \ \ \ \ \ [Number of Tickets]{.math.display}\ {.math.display}\ {.math.display}\ {.math.display}\ {.math.display}\ {.math.display}\ {.math.display}\ {.math.display}\ \ \ \ \ \ \ \ \ [GPA]{.math.display}\ [3.4]{.math.display}\ [3.3]{.math.display}\ [2.4]{.math.display}\ [2.3]{.math.display}\ {.math.display}\ [1.8]{.math.display}\ [1.7]{.math.display}\ -------------------------------------- ------------------------ ------------------------ ------------------------ ------------------------ ---------------------- ------------------------ ------------------------ k. Use your calculator to find the regression line. The linear regression model is: l. Using the regression line, estimate the GPA of a student who had 5 parking tickets. m. Use your calculator to find the coefficient of determination. n. Find the residual of first student. 10. True or False: If the slope of the regression line is negative, then the correlation coefficient must be negative. a. True b. False The scatterplot examines the relationship between the distance (1000s miles) and the time (in hours) for a randomly selected round-trip flight. Use the scatter plot for questions 11 and 12. 11. The relationship between Distance and Time is: a. linear, positive, and strong b. nonlinear, positive, and strong c. linear, negative, and strong d. linear, negative, and weak 12. The dependent variable for the scatterplot is: a. Time (hours) b. Distance (1000s of miles) 13. If the correlation coefficient is r *= 0*, this tells us there is: a. A weak relationship between the two quantitative variables b. A strong relationship between the two quantitative variables c. No linear relationship between the two quantitative variables d. A moderate relationship between the two quantitative variables 14. What is the correlation coefficient, *r*, for the below scatterplot?  a. 0.9999 b. -0.8351 c. 0.0121 d. 0.8351