Project #23570 - Statistics Quiz

 

 

I had to attach the quiz because it wouldn't copy and paste properly onto this site.   

 

I've also attached the book.

 

For the problems that require a written response, please use proper English and complete sentences.  Your definitions and explanations should be explicit and meaningful from a statistical viewpoint.  Where appropriate, fill in the space with the required missing term or value.  For the blanks that are followed by parentheses, select the best answer from within the parenthesis that follows it or from the list below it.  For the computational problems, show all essential work, but please make use of your calculator's statistical keys.  Problem #1 is worth one point, and Problems 2-14 are each worth eight points.  Thus there are a total of 105 points that can be earned on this test with five of those points considered extra credit.  Round all answers appropriately depending upon the type of problem; for instance z-values should be rounded to the nearest hundredth but t-values should be rounded to the nearest thousandth, etc.  Do well!

 

1.  Fill in the blank with the correct selection from the list below.  b, which is pronounced beta, ______.

a)  is the probability of rejecting Ho when in fact Ho is true

b)  is the probability of obtaining a test statistic value beyond the one obtained from a particular sample (and that probability is doubled for a two-tailed test)

c)  is known as the power of the hypothesis test

d)  has a value that increases as the significance level decreases

 

2.  A researcher preformed an initial experiment using 20 mice.  The researcher reported that 35% of the mice were cured of the affliction.  If the CDC wants to be 95% confident that the sample estimate will differ by no more than 4% from the true population proportion, then how large of a sample needs to be taken?  Please state the minimum required sample size.

 

3.  The first blank below should be completed by selecting the appropriate distribution from those given in the parenthesis following the first blank.  The second blank should be completed with the appropriate numerical value or values from the statistical table that corresponds to the answer you provide for the first blank.  The third through fifth blanks should each be completed with appropriate numerical values.

In a random sample of 100 employed UMUC bachelor degree graduates, 62 said that they are employed in the field of their bachelor’s degree.  To construct a 95% confidence interval for the proportion of all employed UMUC bachelor degree graduates who are employed in the field of their degree, the appropriate distribution to use is the _______ (chi-square, F, t, z-standard normal) with a (c2left and c2right, or Fa/2, or ta/2, or za/2 as the case may be) value or values of ___________from the statistical table that corresponds to that distribution (the one stated in the first blank of this sentence.)  The best point estimate of the population proportion of all employed UMUC bachelor degree graduates who are employed in the field of their degree is _______.  Thus, it can be concluded with 95% confidence that between _______ and ________ of all employed UMUC bachelor degree graduates are employed in the field of his/her degree.

 

 

4.  An oceanographer wants to test on the basis of a random sample of size 18 at the 0.05 level of significance, whether the average depth of the ocean in a certain area is 40.6 fathoms, as has been recorded on an old chart.  Assume that the distribution of depth readings has an approximate normal distribution.  To test this chart’s “claim”, the statement of hypothesis is Ho:________ versus H1:________, with the claim located in ________ (fill in this blank with either Ho or with H1 as appropriate).  The appropriate distribution to use to test this claim is the _______ (chi-square, F, t, z-standard normal) and the critical value or values obtained from that distribution is/are ___________ (this blank should be completed with the appropriate numerical value or values of the critical value/s).  If the sample of 18 readings produced a mean of 39.4 fathoms with a standard deviation of 2.2 fathoms, then the computed test statistic value is __________ (complete this blank with the appropriate numerical value of the test statistic), which was computed using _________ (fill in this blank with the appropriate selection from the list of formulas below.)

    a) page 514:     

    b) page 427:

    c) page 496:

    d) page 484:

    e) page 447:

    f) page 437:

    g) page 413:   or  

    h) page 474:    or  

 

 

5.  A new kind of typhoid shot is being developed by a medical research team.  The old typhoid shot was known to protect for a mean of 36 months with a standard deviation of 3 months.  To test the variability of the new shot 24 people were randomly selected and given the new shot.  Regular blood tests of the 24 participants showed a mean protection time of 35 months with a standard deviation of 1.9 months.  The protection times are believed to be normally distributed.  To test the claim that the new typhoid shot has a smaller standard deviation in protection times than the old shot, using a 5% level of significance, the statement of hypothesis is Ho:________ versus H1:________, with the claim located in ________ (fill in this blank with either Ho or with H1 as appropriate).  The appropriate distribution to use to test this claim is the _______ (chi-square, F, t, z-standard normal) and the critical value or values obtained from that distribution is/are ___________ (this blank should be completed with the appropriate numerical value or values of the critical value/s).  The computed test statistic value is __________ (complete this blank with the appropriate numerical value of the test statistic), which was computed using _________ (fill in this blank with the appropriate selection from the list of formulas below.)

    a) page 514:     

    b) page 427:

    c) page 496:

    d) page 484:

    e) page 447:

    f) page 437:

    g) page 413:   or  

    h) page 474:    or  

 

 

6.  An airline claims that its flights land on-time more than 80% of the time.  An aviation agency wants to test that claim using an alpha of 0.05.  A random sample of 50 flights revealed that 84% of that airline’s flights were on time.  The statement of hypothesis is Ho:________ versus H1:________, with the claim located in ________ (fill in this blank with either Ho or with H1 as appropriate).  The appropriate distribution to use to test this claim is the ________ (chi-square, F, t, z-standard normal) and the critical value or values obtained from that distribution is/are ___________ (this blank should be completed with the appropriate numerical value or values of the critical value/s).  The computed test statistic value is __________ (complete this blank with the appropriate numerical value of the test statistic), which was computed using _________ (fill in this blank with the appropriate selection from the list of formulas below.)

    a) page 514:     

    b) page 427:

    c) page 496:

    d) page 484:

    e) page 447:

    f) page 437:

    g) page 413:   or  

    h) page 474:    or  

 

 

 

 

7.  A government testing agency routinely tests various beverages to ensure that they meet label claims.  A random sample of twelve 100-centiliter (cL) labeled bottles of a particular company’s soft drink revealed the actual following amounts (in cL) when tested: 

106   86    95    88    90    89    99    95    79    102   102   97

Note that the distribution of fill amounts can be assumed to be approximately normal.  To construct a 95% confidence interval for the mean amount actually contained in all 100 cL labeled bottles of the soft drink manufactured by this company, the appropriate distribution to use is the _______ (chi-square, F, t, z-standard normal) with a (c2left and c2right, or Fa/2, or ta/2, or za/2 as the case may be) value or values of ___________________from the statistical table that corresponds to that distribution (the one stated in the first blank of this sentence.)  The best point estimate of the population mean is _______ cL and the sample standard deviation is ______ cL.  Hence, we can be 95% that the true average amount of soft drink contained in 100 cL labeled bottles of this company is between _______ cL and ______ cL.

 

 

8.  A company is experimenting with marketing advertisements delivered by phone calls.  Of primary concern is how much of a pre-recorded 7-minute advertisement is heard.  In a random sample of 16 calls a mean of 1.85 minutes of the ad was ‘heard’ with a standard deviation of 1.4 minutes.  An employee, who had taken STAT 200 while in college, suggested the mean length of time the advertisement is heard would increase if a catchy tune is played softly throughout the advertisement.  To test this employee’s claim (although he/she should be able to test it him/herself), a random sample of 30 new calls revealed a mean length of time the advertisement ran before the listeners hung-up was 2.3 minutes with a standard deviation of 0.8 minutes.  To test the claim that the mean length of time the advertisement is heard with music is greater than the mean time without the music, it was assumed that the distributions of ‘listening’ times for both scenarios were approximately normally distributed with unequal population variances.  The null hypothesis is Ho:________ and the alternative hypothesis is H1:________, with the claim located in ________ (fill in this blank with either Ho or with H1 as appropriate).  The appropriate distribution to use to test this claim is the ________ (chi-square, F, t, z-standard normal) and using a 0.05 significance level the critical value or values obtained from that distribution is/are ___________ (this blank should be completed with the appropriate numerical value or values of the critical value/s).  Furthermore, the test statistic value is calculated to be __________ (complete this blank with the appropriate numerical value of the test statistic), which was computed using _________ (fill in this blank with the appropriate selection from the list of formulas below.)

    a) page 514:     

    b) page 427:

    c) page 496:

    d) page 484:

    e) page 447:

    f) page 437:

    g) page 413:   or  

    h) page 474:    or  

 

 

9.  Refer to the previous problem about the telephone marketing schemes above.  An assumption was made that the distributions of ‘listening’ times for both scenarios were approximately normally distributed with unequal population variances.  To test that assumption, using a 0.05 level of significance, that the population variances are different, the statement of hypothesis is Ho:________ versus H1:________, with the claim located in ________ (fill in this blank with either Ho or with H1 as appropriate).  The appropriate distribution to use to test this claim is the ________ (chi-square, F, t, z-standard normal) and the critical value or values obtained from that distribution is/are ___________ (this blank should be completed with the appropriate numerical value or values of the critical value/s).  The computed test statistic value is __________ (complete this blank with the appropriate numerical value of the test statistic), which was computed using _________ (fill in this blank with the appropriate selection from the list of formulas below.)

    a) page 514:     

    b) page 427:

    c) page 496:

    d) page 484:

    e) page 447:

    f) page 437:

    g) page 413:   or  

    h) page 474:    or  

 

 

 

10. The variance in weights of all parcels sent via National Express is 60.84 pounds2.  A random sample of 40 parcels mailed National Express from various APO’s revealed a sample mean weight of 23.1 pounds and a standard deviation of 7.8 pounds.  In order to construct a 95% confidence interval for mean weight of all parcels sent National express form APO’s such that the true mean differs from the sample mean by no more than 1.5 pounds, then how large of a sample size is needed?  Note that due to cost constraints the minimum required sample size needed should be stated for your answer.

 

 

 

 

 

11. The Home Construction Company is looking for ways to reduce the cost of homes they build.  As a possible cost saving measure they invite two manufacturers of kitchen cabinets to offer bids (in dollars) to install kitchen cabinets in a sample of seven randomly selected homes under construction.  The bids received for each of the seven homes by the two manufactures are: 

Home #:                 1     2     3     4     5     6     7

Kabinet Kitchens (KK): 480    660   525   489   668   751   555

Cupboard Cabinets(CC): 530    650   525   522   677   740   589

Based upon the data and upon the assumption that the distribution of bids made by the two cabinet manufacturers are approximately normally distributed, test the claim, at the 5% significance level, that the average bid by manufacture KK will be less expensive than manufacturer CC to install cabinets for all the homes that the Home Construction Company constructs by answering the following.  The statement of hypothesis is Ho:________ versus H1:________, with the claim located in ________ (fill in this blank with either Ho or with H1 as appropriate).  The appropriate distribution to use to test this claim is the ________ (chi-square, F, t, z-standard normal) and the critical value or values obtained from that distribution is/are ___________ (this blank should be completed with the appropriate numerical value or values of the critical value/s).  The appropriate formula to use to compute the test statistic value is _________ (fill in this blank with the appropriate selection from the list of formulas below.)

    a) page 514:     

    b) page 427:

    c) page 496:

    d) page 484:

    e) page 447:

    f) page 437:

    g) page 413:   or  

    h) page 474:    or   

 

 

 

12. A meteorologist who sampled 13 thunderstorms found that the average speed at which they traveled across a certain state was 15 mph and that standard deviation of those thunderstorms was calculated to be 1.7 mph.  Assuming that the distribution of thunderstorm speeds across that state is approximately normally distributed, if we were to construct a 95% confidence interval for the variance in the speeds of all thunderstorms across that state, then the formula that should be utilized is ______________ (a list is provided below to make it easier to state your answer for this blank).  If your answer to the preceding blank was a or b then za/2=_____, or if your answer was c then ta/2= ______, however if your answer was d or e, then chi-square values are ______ and ______.

a)  page 359:  

b)  page 378:  

c)  page 371:  

d)  page 388 1st:  

e)  page 388 2nd:

 

 

 

13. The mean grade point average (GPA) for one particular college is 2.85 with a standard deviation of 0.63.  A fine arts professor believes that fine arts majors have a higher grade point average than the college’s mean.  To test the professor’s claim, the statement of hypothesis is Ho:_______ versus H1:_______ with the claim located in ______ (fill in this blank with Ho or H1 as appropriate).  If the critical value is found to be 2.31 and the test statistic value was computed to be 2.54 based upon a random sample of fine arts majors at this particular college, then the appropriate decision is to ______________ (accept Ho, accept H1, reject Ho, reject H1) and the appropriate conclusion is ______ (fill in this blank with the appropriate response from the list below.)

a)  The GPA of all fine arts majors at this college is significantly less than 2.85.

b)  The GPA of all fine arts majors at this college is not significantly less than 2.85.

c)  The GPA of all fine arts majors at this college is significantly greater than 2.85.

d)  The GPA of all fine arts majors at this college is not significantly greater than 2.85.

e)  The GPA of all fine arts majors at this college is significantly different from 2.85.

f)  The GPA of all fine arts majors at this college is not significantly different from 2.85.

 

 

 

 

14. Two different models of cars were tested for gas mileage.  The claim was made that the two models have the same average gas mileage.  Random samples of 45 cars each were used to collect sample data.  The p-value was computed to be 0.062.  In a test of the claim the statement of hypothesis is Ho:_______ versus H1:_______ with the claim located in ______ (fill in this blank with Ho or H1 as appropriate).  At the 5% level of significance the appropriate decision is to ___________ (accept Ho, accept H1, reject Ho, reject H1) although there could exist a _________________ (margin of error, standard error, Type I error, Type II error).

Subject Mathematics
Due By (Pacific Time) 02/26/2014 10:00 pm
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