Jonathan considers booking a flight to see the temple at Chichen

Jonathan considers booking a flight to see the temple at Chichen

Subject: Mathematics    / Statistics
Question
Jonathan considers booking a flight to see the temple at Chichen Itza, which is near Cancun Mexico. Expedica.ca offers both business class (non-stop/direct) as well as first class flights (with a 1-stop layover). Jonathan wants to know if the prices for his options are approximately the same, or if flying first class will generally cost more. Can you help him find this out? Use ?=0.033?=0.033for all calculations. The specifics can be found in the file below.
Download .csv file(a) Check to see if the distribution of the flight classes appear to be normal. Hint: use a probability plot to decide with ?=0.033?=0.033.
A. neither direct flights nor layover flights appear to be normal
B. direct flights appear to be normal but layover flights do not appear to be normal
C. layover flights appear to be normal but direct flights do not appear to be normal
D. Both direct flights and layover flights appear to be normal
(b) Report the p-value of the test you ran in (a) concerning the normality of first class flights, use at least two decimals in your answer.
P-value =
equation editorEquation Editor(c) Does there appear to be a negative difference in the general price between business and first class flights?
A. I don’t have enough information to answer this questionB. YesC. NoD. I have too much information to answer this question
(d) At what level of significance would you come to a different conclusion? Please use at least four digits in your answer. Give a decimal not a percentage.
Significance Level = equation editorEquation Editor(e) Based on the above calculations, to save money Jonathan should
a buy a business class (direct) flight
b buy a first class (layover) flight
c buy a business class (layover) flight
d buy a first class (direct) flight
e buy either a first or business class flight, since the difference is negligibleA professor in the school of business at a certain university wants to investigate the claim that the prices of new textbooks in the campus store are higher than a competing national online bookstore. The professor randomly chooses required texts for 12 business school courses. The data is given in the table below.Book
Campus Store
Online Store
A
51.96
51.12
B
180.82
177.78
C
109.66
107.78
D
206.53
207.37
E
176.23
175.88
F
56.61
55.01
G
180.73
183.06
H
179.45
175.15
I
193.27
193.66
J
111.81
110.45
K
129.91
129.72
L
110.77
110.27
2 (a) Let XAXA denote the price of books at the campus store, and XBXB be the price of books at the online store, also let XD=XA?XBXD=XA?XB. Choose the correct statistical hypotheses.
A. H0:?D>0,HA:?D<0H0:?D>0,HA:?D<0
B. H0:?D=0,HA:?D<0H0:?D=0,HA:?D<0
C. H0:?campus=?online,HA:?campus<?onlineH0:?campus=?online,HA:?campus<?online
D. H0:?D=0,HA:?D?0H0:?D=0,HA:?D?0
E. H0:?campus=?online,HA:?campus>?onlineH0:?campus=?online,HA:?campus>?online
F. H0:?D=0HA:?D>0H0:?D=0HA:?D>0
G. H0:?D=0,HA:?D<0H0:?D=0,HA:?D<0
H. H0:?campus=?online,HA:?campus??onlineH0:?campus=?online,HA:?campus??online
(b) Carry out the appropriate statistical test and find the PP-value, to at least three decimal places.
P=equation editorEquation Editor
(c) Based on the above calculations, we should (reject/not reject)the null hypothesis. Use ?=0.05
(d) Using the technology available to you, create the most appropriate graph(s) to check the assumption(s) that need to be satisfied for your inferences in (b) and (c) to be valid. What statement below aligns with your findings?
A. The prices charged at the online bookstore are normally distributed.
B. The prices charged at the campus bookstore are normally distributed.
C. The prices charged at the campus bookstore are not normally distributed.
D. The differences in the price of a textbook at the campus bookstore and the price of the textbook at the online store are not normally distributed.
E. The prices charged at the online bookstore are not normally distributed.
F. The differences in the price of a textbook at the campus bookstore and the price of the textbook at the online store are normally distributed3
To compare the effectiveness of a media campaign – via radio ads, billboards, and ads on social media websites – to reduce the incidence of impaired driving, a police chief inspected data from 60 randomly chosen CheckStops at varying locations.Thirty of these were before the launch of this campaign, 30 were after the media campaign had been running for a months time. Use?=0.05?=0.05for all calculations.For each CheckStop randomly chosen, the number of people charged with impaired driving was recorded:
Prior: 10, 4, 3, 9, 4, 4, 7, 10, 7, 6, 6, 6, 4, 5, 2, 5, 13, 12, 4, -1, 6, 8, 6, 5, 4, 7, 6, 12, 4, 2;
After: 4, 7, 5, 5, 4, 4, 8, 7, 4, 6, 3, 3, 5, 7, 5, 7, 7, 7, 4, 5, 6, 4, 11, 7, 3, 7, 3, 4, 4, 5;
Let?Before?Beforerepresent the mean number of impaired driving charges at a checkstop prior to the launch of the campaign, and?After?Afterbe the mean number of impaired driving charges at a checkstop after the campaign has been running for a month.(a) Does this data suggest that the variation in the number of impaired driving charges before the campaign is equal to the variation in the number of impaired driving charges after the campaign has been running for a month?
From the appropriate statistical test, find the value of the test statistic. Using at least two decimals in your answer.
Test Statistic = equation editorEquation Editor
(b) Report the p-value of the test you ran in (a), using at least three decimals in your answer.
P-value = equation editorEquation Editor
(c) Testing at?=0.05?=0.05, the null hypothesis in (a) would
be rejected/not be rejected
The variation in the distribution of the number of impaired driving charges before the campaign is statistically
the same/not the same
as the variation distribution of the number of impaired driving charges after the campaign has been running for a month.(d) Using your findings in part (c), find a 95% confidence interval for the difference between the mean number of impaired driving charges before the media campaign and the mean number of impaired driving charges after the media campaign has been running for a month,?Before??After?Before??After.Lower Bound of 95% CI =
(use at least three decimals)Upper Bound of 95% CI =
(use at least three decimals)(e) The confidence interval found in part (d) indicates that the average number of impaired driving charges before the launch of the campaign is
higher/lower/the same
the mean number of impaired driving charges after the campaign has been running for a month.
4(see file 2652f83f032)
Samuel has two different methods to make money off of the stock market, but he doesn’t know which method is better, so he tried both methods for one year. On the one hand plan 1 (SP1) made on averageX¯¯¯¯1=13.96X¯1=13.96dollars per week, where plan 2 (SP2) made an averageX¯¯¯¯2=14.77X¯2=14.77dollars per week. The downside of plan 1, however, seems to be that the standard deviation,s1=21.57s1=21.57is greater then plan 2’s and once he even had a minimum of -19.97 dollars one week. Plan 2 appears to be more conservative,s2=17.37s2=17.37and the lowest amount made in a week was -13.22. Can you help him find out whether these two plans are statistically similar? In all cases use SP1 as sample 1. The specifics can be found in the file below.
(a) Check to see if the distribution of the stock plans appear to be normal. Hint: use a probability plot to decide and an alpha = 0.05
A. neither plan 1 appear to be normal nor plan 2 appear to be normalB. plan 2 appears to be normal but plan 1 does not appear to be normalC. Both plan 1 and plan 2 appear to be normalD. plan 1 appears to be normal but plan 2 does not appear to be normal
(b) Report the p-value of the test you ran in (a) concerning the normality of plan 2 use exactly two decimals in your answer.
P-value = equation editorEquation Editor
(c) Does there appear to be a statistical difference between Stock Plan 1 and Stock Plan 2? (Remember to use CLT if applicable)
A. I have too much information to answer this questionB. NoC. YesD. I don’t have enough information to answer this question
(d) Report the test statistic value you ran in (c). Use at least two decimals in your answer. equation editorEquation Editor
(e) Report the p-value of the test you ran in (c). Use at least three decimals in your answer.
P-value = equation editorEquation Editor5
A student project involved collecting data to see if there was a difference in the amount of time one had to wait at the drive-thru between two fast food restaurants, A and B. She randomly selected 17 cars at fast food restaurant A and 17 cars at fast food restaurant B. For each car chosen, she recorded how much time passed from the placement of the order to receiving their food at the pick-up window. The data is given in the table below measured in Seconds. Use ?=0.05?=0.05.Fast Food A
Fast Food B
198.7
145.9
168.7
211.2
215.7
147.8
188.5
185.4
211.7
214.1
188.2
182.8
209.2
154.1
231
125.5
198.8
222.5
191.4
145.8
178.3
218.8
193.6
85.9
194.9
130.8
167.4
114.9
219.4
210.9
235.2
243.1
222.4
303Download .csv file(a) Choose the most appropriate statistical hypotheses.
A. H0:?A=?BHA:?A<?BH0:?A=?BHA:?A<?B
B. H0:?A=?BHA:?A??BH0:?A=?BHA:?A??B
C. H0:?D=0,HA:?D>0H0:?D=0,HA:?D>0
D. H0:?A=?BHA:?A>?BH0:?A=?BHA:?A>?B
E. H0:?D=0,HA:?D<0H0:?D=0,HA:?D<0
F. H0:?D=0,HA:?D?0H0:?D=0,HA:?D?0
(b) Test the statistical hypotheses in (a) by carrying out the appropriate statistical test. Find the value of the test statistic for this test, use at least two decimals in your answer.
Test Statistic = equation editorEquation Editor
(c) Determine the PP-value for this test, to at least three decimal places.
P=P=equation editorEquation Editor
(d) Based on the above calculations, we shouldreject/not reject the null hypothesis. Use ?=0.056
Ken and Billy both live in the same neighborhood, and work at the university. Ken drives to work, Billy rides his bicycle. You – a budding statistician – have been asked to settle an argument. Ken believes that more often than not, his commuting time via his drive is less than Billy’s. Billy believes that this is not so, due to traffic volume and traffic lights. Over the period of one month, the statistician randomly selects eight days for Ken and eight days for Billy. On each day, they will be asked to measure, to the nearest tenth of a minute, the amount of time it takes them to get from their home to the university campus.The commuting times are given on each randomly chosen day, for each person.Ken: 24, 13.6, 9.7, 21.6, 13.8, 10.6, 9.6, 14.9;
Billy: 20.4, 20.3, 20.1, 17.1, 16.8, 19.8, 19.9, 17.1;Carry out a statistical test, the results of which will be used to settle Ken and Billy’s argument.(a) Using the technology available to you, visually and statistically inspect this data. From this, construct the most appropriate statistical hypotheses.
A. H0:?D=0HA:?D<0H0:?D=0HA:?D<0B. H0:?D=0HA:?D>0H0:?D=0HA:?D>0C. H0:?D=0HA:?D?0H0:?D=0HA:?D?0D. H0:?Ken=?BillyHA:?Ken<?BillyH0:?Ken=?BillyHA:?Ken<?BillyE. H0:?Ken=?BillyHA:?Ken>?BillyH0:?Ken=?BillyHA:?Ken>?BillyF. H0:?~Ken=?~BillyHA:?~Ken??~BillyH0:?~Ken=?~BillyHA:?~Ken??~BillyG. H0:?~Ken=?~BillyHA:?~Ken>?~BillyH0:?~Ken=?~BillyHA:?~Ken>?~BillyH. H0:?~Ken=?~BillyHA:?~Ken<?~BillyH0:?~Ken=?~BillyHA:?~Ken<?~BillyI. H0:?Ken=?BillyHA:?Ken??BillyH0:?Ken=?BillyHA:?Ken??Billy
(b) Find the value of the test statistic for this test, use at least one decimal in your answer.
Test Statistic = equation editorEquation Editor
(c) Determine thePP-value of your statistical test in part (c), and report it to at least three decimal places.
P=
(d) At?=0.05?=0.05, this data indicates that you will
reject/not reject
the null hypothesis. You can tell Ken that his commute time is
same as/faster than/slower than
Billy’s.7 (see file 45f1325371e)
There has been an alcohol war between Bob and Len for some time now. The following results were observed. Does the data indicate that the average purchases at Lenâs exceed, on average, those at Bobâs by more than 8.50 dollars? The data is given in the file below. Use ?=0.094?=0.094 for all calculations.
Download .csv file
And is summarized here
Bobs Booze
Lens Liquor Emporium
n
46
39
average cost
49.38
58.99
variance of cost
10.19
3.46
(a) Form the correct hypothesis
A. H0:?Len??Bob=8.5HA:?Len??Bob?8.5H0:?Len??Bob=8.5HA:?Len??Bob?8.5B. H0:?Len=?BobHA:?Len>?BobH0:?Len=?BobHA:?Len>?BobC. H0:?Len??Bob=8.5HA:?Len??Bob>8.5H0:?Len??Bob=8.5HA:?Len??Bob>8.5D. H0:?Len??Bob=8.5HA:?Len??Bob<8.5H0:?Len??Bob=8.5HA:?Len??Bob<8.5E. H0:?Len=?BobHA:?Len<?BobH0:?Len=?BobHA:?Len<?BobF. H0:?Len=?BobHA:?Len??BobH0:?Len=?BobHA:?Len??Bob
(b) (i) Using technology available to you, test to see if the variances are equal or not?
A. There appears to be more variation in Lens sales than in the Bobs.B. They appear to be equal.C. There appears to be more variation in Bobs sales than in the Lens.
(b) (ii)Report the p-value of the test you ran in (b)(i) use at least three decimals in your answer.
P-value = equation editorEquation Editor
(c) Test the statistical hypotheses in (a) by carrying out the appropriate statistical test. Find the value of the test statistic for this test, use at least two decimals in your answer.
Value of the test statistic = equation editorEquation Editor
(d) Determine thePP-value for the difference of means test, and report it to at least three decimal places.
P=P= equation editorEquation Editor
(e) Determine the appropriate degrees of freedom for this test. As an integer.
DF= equation editorEquation Editor
(f) Based on the above calculations, we should
reject/not reject
the null hypothesis.8 (see file 2d8632e93fcf)
Two marathon training procedures are tried for comparison purposes. Their efficacy is to be determined in a marathon race. Assume race times are given in minutes. Use?=0.058?=0.058for all calculations.The following results were observed:. The data is given in the file below.
Download .csv file(a) Do the populations appear to be normal? Hint: use a probability plot to decide
A. Yes, procedure A appears to be normal but procedure B does not appear to be normalB. Yes, Both procedure A and procedure B appear to be normalC. Yes, Both procedure A and procedure B appear to be non-normalD. No, Both procedure A and procedure B appear to be normalE. Yes, procedure B appears to be normal but procedure A does not appear to be normalF. No, neither procedure A appears to be normal nor procedure B appears to be normal
(b) Choose the most appropriate statistical hypotheses to see which procedure results in longer marathon times (be very careful in how you formulate your hypothesis, this one is tricky! Use the sample data to make any assumptions necessary.)
A. H0:?1=?2HA:?1??2H0:?1=?2HA:?1??2B. H0:?1=?2HA:?1<?2H0:?1=?2HA:?1<?2C. H0:?D=0,HA:?D<0H0:?D=0,HA:?D<0D. H0:?D=0,HA:?D>0H0:?D=0,HA:?D>0E. H0:?1=?2HA:?1>?2H0:?1=?2HA:?1>?2F. H0:?D=0,HA:?D?0H0:?D=0,HA:?D?0
(c) Using technology available to you, test to see if the variances are equal or not?
A. They appear to be equal.B. There appears to be more variation in the 2nd procedure then in the 1st.C. There appears to be more variation in the 1st procedure then in the 2nd.D. There appears to be an unequal amount of variation in the 2nd procedure then in the 1st.
(d) Report the p-value of the test you ran in (c) use at least three decimals in your answer (this is from Levene’s test).
P-value = equation editorEquation Editor
(e) Test the statistical hypotheses in (b) by carrying out the appropriate statistical test. Find the value of the test statistic for this test, use at least two decimals in your answer (from your test of middle).
Test Statistic = equation editorEquation Editor
(f) Determine thePP-value for this test, to at least three decimal places (from your test of middle).
P=P= equation editorEquation Editor
(g) Based on the above calculations, we should
reject/not reject
the null hypothesis.