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MATH225 Week 8 Final Exam
Question 1 1/1 points A fitness center claims that the mean amount of time that a person spends at the gym per visit is 33 minutes. Identify the null hypothesis, H 0 , and the alternative hypothesis, Ha , in terms of the parameter μ. That is correct! H 0 : μ ≠33; Ha : μ = H 0 : μ =33; Ha : μ ≠ H 0 : μ ≥33; Ha : μ < H 0 : μ ≤33; Ha : μ > Answer Explanation Correct answer: H 0 : μ =33; Ha : μ ≠ Let the parameter μ be used to represent the mean. The null hypothesis is always stated with some form of equality: equal (=), greater than or equal to (≥), or less than or equal to (≤). Therefore, in this case, the null hypothesis H 0 is μ =33. The alternative hypothesis is contradictory to the null hypothesis, so Ha is μ ≠33. Question 2 1/1 points The answer choices below represent different hypothesis tests. Which of the choices are right- tailed tests? Select all correct answers. That is correct!
H 0: X ≥17.1, Ha : X <17. H 0: X =14.4, Ha : X ≠14. H 0: X ≤3.8, Ha : X >3. H 0: X ≤7.4, Ha : X >7. H 0: X =3.3, Ha : X ≠3. Answer Explanation Correct answer: H 0: X ≤3.8, Ha : X >3. H 0: X ≤7.4, Ha : X >7. Remember the forms of the hypothesis tests. Right-tailed: H 0: X ≤ X 0 , Ha : X > X 0.
structures were built without permits when, in fact, more than 15% of the structures were built without permits. Question 4 1/1 points Suppose a chef claims that her meatball weight is less than 4 ounces, on average. Several of her customers do not believe her, so the chef decides to do a hypothesis test, at a 10% significance level, to persuade them. She cooks 14 meatballs. The mean weight of the sample meatballs is 3. ounces. The chef knows from experience that the standard deviation for her meatball weight is 0.5 ounces. H 0 : μ ≥4; Ha : μ < α =0.1 (significance level) What is the test statistic ( z -score) of this one-mean hypothesis test, rounded to two decimal places? That is correct! Test statistic = minus 2 point 2 4$$ Test statistic = minus 2 point 2 4 - correct Answer Explanation Correct answers: Test statistic = minus 2 point 2 4 $\text{Test statistic = }-2.24$ The hypotheses were chosen, and the significance level was decided on, so the next step in hypothesis testing is to compute the test statistic. In this scenario, the sample mean weight, x ¯=3.7. The sample the chef uses is 14 meatballs, so n =14. She knows the standard deviation of the meatballs, σ =0.5. Lastly, the chef is comparing the population mean weight to 4 ounces. So, this value (found in the null and alternative hypotheses) is μ 0. Now we will substitute the values into the formula to compute the test statistic:
z 0= x ¯− μ 0 σn √=3.7−40.514√≈−0.30.134≈−2. So, the test statistic for this hypothesis test is z 0=−2.24. Question 5 · 1/1 points What is the p -value of a right-tailed one-mean hypothesis test, with a test statistic of z 0=1.74? (Do not round your answer; compute your answer using a value from the table below.) z1.51.61.71.81.90.00 0.9330.9450.9550.9640.971 0.01 0.9340.9460.9560.9650.972 0.02 0.9360. 0.9570.9660.973 0.03 0.9370.9480.9580.9660.973 0.04 0.9380.9490.9590.9670.974 0.05 0.9390. 0.9600.9680.974 0.06 0.9410.9520.9610.9690.975 0.07 0.9420.9530.9620.9690.976 0.08 0.9430. 0.9620.9700.976 0.09 0.9440.9540.9630.9710. That is correct! 0 point 0 4 1$$ 0 point 0 4 1 - correct Answer Explanation Correct answers: 0 point 0 4 1 $0.041$ The p -value is the probability of an observed value of z=1.74 or greater if the null hypothesis is true, because this hypothesis test is right-tailed. This probability is equal to the area under the Standard Normal curve to the right of z =1.74.
That is correct! Do not reject the null hypothesis because the p -value 0.0401 is greater than the significance level α =0.04. Reject the null hypothesis because the p -value 0.0401 is greater than the significance level α =0.04. Reject the null hypothesis because the value of z is negative. Reject the null hypothesis because |−1.75|>0.04. Do not reject the null hypothesis because |−1.75|>0.04. Answer Explanation Correct answer: Do not reject the null hypothesis because the p -value 0.0401 is greater than the significance level α =0.04. In making the decision to reject or not reject H 0 , if α > p -value, reject H 0 because the results of the sample data are significant. There is sufficient evidence to conclude that H 0 is an incorrect belief and that the alternative hypothesis, Ha , may be correct. If α ≤ p -value, do not reject H 0. The results of the sample data are not significant, so there is not sufficient evidence to conclude that the alternative hypothesis, Ha , may be correct. In this case, α =0.04 is less than or equal to p =0.0401, so the decision is to not reject the null hypothesis. Question 45 · 1/1 points Fill in the following contingency table and find the number of students who both do not play sports AND do not play an instrument. StudentsplaysportsdonotplaysportsTotalplayaninstrument33donotplayaninstrument69Total
That is correct! 34$$ 34 - correct Answer Explanation Correct answers: 34 $34$ By using the known totals along the rows and columns you can fill in the rest of the contingency table. For example, looking at the second row in the table, we know that 33 added to the unknown number in the middle is 67 , so that unknown number is 34. Continuing in this way, we can fill in the entire table: StudentsplaysportsdonotplaysportsTotalplayaninstrument273360donotplayaninstrument353469T otal From this, we can see that the number of students who both do not play sports and do not play an instrument is 34. Question 46 · 1/1 points The answer choices below represent different hypothesis tests. Which of the choices are left- tailed tests? Select all correct answers. That is correct! H 0: X =17.3, Ha : X ≠17.
H 0: X ≥11.2, Ha : X <11. H 0: X ≥19.7, Ha : X <19. Question 47 · 1/1 points Assume the null hypothesis, H 0 , is: Jacob earns enough money to afford a luxury apartment. Find the Type I error in this scenario. That is correct! Jacob thinks he does not earn enough money to afford the luxury apartment when, in fact, he does. Jacob thinks he does not earn enough money to afford the luxury apartment when, in fact, he does not. Jacob thinks he earns enough money to afford the luxury apartment when, in fact, he does not. Jacob thinks he earns enough money to afford the luxury apartment when, in fact, he does. Answer Explanation Correct answer: Jacob thinks he does not earn enough money to afford the luxury apartment when, in fact, he does. A Type I error is the decision to reject the null hypothesis when it is true. In this case, the Type I error is when Jacob thinks he does not earn enough money when he really does.
Question 48 · 1/1 points Given the plot of normal distributions A and B below, which of the following statements is true? Select all correct answers. A normal bell curve labeled Upper A and a normal elongated curve labeled Upper B are centered at the same point. Normal curve Upper B is narrower and above normal curve Upper A. That is correct! A has the larger mean. B has the larger mean.
the graph will be tall and skinny. Because A is shorter and more spread out than B , we find that A has the larger standard deviation. Question 49 · 1/1 points Hugo averages 62 words per minute on a typing test with a standard deviation of 8 words per minute. Suppose Hugo's words per minute on a typing test are normally distributed. Let X = the number of words per minute on a typing test. Then, X ∼ N (62,8). Suppose Hugo types 56 words per minute in a typing test on Wednesday. The z -score when x = is ________. This z -score tells you that x =56 is ________ standard deviations to the ________ (right/left) of the mean, ________. Correctly fill in the blanks in the statement above. That is correct! Suppose Hugo types 56 words per minute in a typing test on Wednesday. The z -score when x = is 0.75. This z -score tells you that x =56 is 0.75 standard deviations to the right of the mean, 62. Suppose Hugo types 56 words per minute in a typing test on Wednesday. The z -score when x = is −0.75. This z -score tells you that x =56 is 0.75 standard deviations to the left of the mean, 62. Suppose Hugo types 56 words per minute in a typing test on Wednesday. The z -score when x = is 0.545. This z -score tells you that x =56 is 0.545 standard deviations to the right of the mean, 62.
Suppose Hugo types 56 words per minute in a typing test on Wednesday. The z -score when x = is −0.545. This z -score tells you that x =56 is 0.545 standard deviations to the left of the mean, 62. Answer Explanation Correct answer: Suppose Hugo types 56 words per minute in a typing test on Wednesday. The z -score when x = is −0.75. This z -score tells you that x =56 is 0.75 standard deviations to the left of the mean, 62. The z -score can be found using the formula z = x − μσ =56−628=−68≈−0. A negative value of z means that that the value is below (or to the left of) the mean, which was given in the problem as μ =62 words per minute in a typing test. The z -score tells you how many standard deviations the value x is above (to the right of) or below (to the left of) the mean, μ. So, typing 56 words per minute is 0.75 standard deviations away from the mean. Question 50 · 1/1 points The following frequency table summarizes a set of data. What is the five-number summary? Value Frequency 1 6 2 2 3 1 4 1 8 1 9 1 10 1 16 6 20 3
value of that half of the data is $2$. This is the first quartile. Similarly, the third quartile is the median of the upper half of the data, which is $20$. $\color{blue}{1}$, $1$, $1$, $1$, $1$, $1$, $\color{blue}{2}$, $2$, $3$, $4$, $8$, $9$, $10$, $\color{blue}{16}$, $16$, $16$, $16$, $16$, $16$, $20$, $\color{blue}{20}$, $20$, $21$, $23$, $24$, $25$, $
color{blue}{27}$ So, the five-number summary is Min Q1 Median Q3 Max $1$ $2$ $16$ $20$ $27$
MATH225 Week 8 Final Exam (Version 4)
Question
Which of the following data sets or plots could have a regression line with a negative slope? Select all that apply. Great work! That's correct. the difference in the number of ships launched by competing ship builders as a function of the number of months since the start of last year the number of hawks sighted per day as a function of the number of days since the two-week study started the total number of ships launched by a ship builder as a function of the number of months since the start of last year the average number of hawks sighted per day in a series of studies as a function of the number of days since the ten-week study started
Answer Explanation
Correct answer:
A scatterplot has a horizontal axis labeled Year from 2005 to 2015 in increments of 5 and a vertical axis labeled Price ($) from 2660 to 2780 in increments of 20. The following points are plotted: (2003, 2736); (2004, 2715); (2007, 2675); (2009, 2719); (2013, 270). All coordinates are approximate. Interpret the slope of the least squares regression line. Yes that's right. Keep it up! The average cost of a designer jacket decreased by $3.765 each year between 2000 and 2015. The average cost of a designer jacket increased by $3.765 each year between 2000 and 2015. The average cost of a designer jacket decreased by $ 4815 each year between 2000 and 2015. The average cost of a designer jacket increased by $ 4815 each year between 2000 and 2015.
Answer Explanation
Correct answer:
The average cost of a designer jacket increased by $3.765 each year between 2000 and 2015.
Since the slope of the line is positive 3.765, the average increase in cost is $3.765 per year.
Question
The scatter plot below shows data for the average cost of a high-end computer (y, in dollars) in
the year x years since 2000. The least squares regression line is given by yˆ=− 1677 + 314 x.
A coordinate plane has a horizontal x-axis labeled Year from 4 to 12 in increments of 2 and a vertical y-axis labeled Cost in dollars from 0 to 2000 in increments of 500. The following points are plotted: left-parenthesis 6 comma 250 right-parenthesis, left-parenthesis 7 comma 550 right- parenthesis, left-parenthesis 9 comma 1000 right-parenthesis, left-parenthesis 10 comma 1300 right-parenthesis, and left-parenthesis 11 comma 2000 right-parenthesis. A line rises from left to right, passing through left-parenthesis 7 comma 550 right-parenthesis and left-parenthesis 10 comma 1500 right-parenthesis. All coordinate are approximate. Interpret the slope of the least squares regression line. Great work! That's correct. On average, the average cost of a high-end computer is predicted to decrease by $ 314 each year. On average, the average cost of a high-end computer is predicted to increase by $ 314 each year. The average cost of a high-end computer increases by $ 314 each year. On average, the average cost of a high-end computer is predicted to decrease by $ 1677 each year.
Answer Explanation
Correct answer:
On average, the average cost of a high-end computer is predicted to increase by $ 314 each year.
Since the slope of the line is positive 314 , on average, the average cost of a high-end computer
is predicted to increase by $ 314 each year.
Question
Which of the following data sets or plots could have a regression line with a negative slope?
