Suppose there is a linear association between crime rate and percentage of high school graduates.

a) State the full and reduced model

b)Obtain SSE(F), SSE(R), df(F), fd(R), test statistics F for the general linear test and decision rule.

crime rate, high school grad %

  8487    74
   8179    82
   8362    81
   8220    81
   6246    87
   9100    66
   6561    68
   5873    81
   7993    74
   7932    82
   6491    75
   6816    82
   9639    78
   4595    84
   5037    82
   4427    79
   6226    78
  10768    73
   8335    77
  12311    65
  10104    77
  10503    76
   7562    79
   8593    79
   7133    78
  10205    84
  14016    78
   5959    81
   3764    89
   4297    85
   7562    77
   4844    74
   5777    80
   3599    84
   3219    88
  11187    75
   2105    77
   6650    78
  11371    61
   4517    91
   7348    83
   5696    77
   4995    85
   9248    70
   6860    88
   9776    80
   4280    82
  11154    82
   3442    82
   9674    70
   7309    64
   4530    79
   4017    83
   7122    77
   5689    76
   6109    80
   3343    84
   5029    82
   4330    81
   5425    74
   8769    81
   6880    76
   6538    78
   6521    78
   9423    79
   9697    83
   3805    79
   3134    83
   3433    81
   2979    84
   6836    64
   5804    67
   7986    75
  10994    73
  11322    77
   8937    64
   8807    75
  11087    80
  10355    83
   7858    85
   3632    91
   8040    88
   6981    83
   7582    76

When 41 people are used the Weight Watchers diet for one year, their weight losses had a standard deviation of 4.9lb. Use a 0.01 significance level to test the claim that the amounts of weight loss have a standard deviation equal to 6.0lb, which appears to be the standard deviation for the amounts of weight loss with the Zone diet. Write your assumptions before you conduct hypothesis testing.

Below you have a payoff table for a set of decisions that are under consideration.

                                               States of Nature

Alternative                  Low          High

Option A                     10              15

Option B                     12              13

Option C                     13               10

Choose the correspondence equation line for option A, B, and C:

Y= -5x+15x

Y=3x+10

Y=-X+13

In a study of computer use, 1000 randomly selected Canadian Internet users were asked how much time they spend using the Internet in a typical week. The mean of the sample observations was 12.9 hours.

(a) The sample standard deviation was not reported, but suppose that it was 6 hours. Carry out a hypothesis test with a significance level of 0.05 to decide if there is convincing evidence that the mean time spent using the Internet by Canadians is greater than 12.7 hours. (Use a statistical computer package to calculate the P-value. Round your test statistic to two decimal places and your P-value to three decimal places.)

t= P-value =

State the conclusion in the problem context.

a. Reject H₀. We have convincing evidence that the mean weekly time spent using the Internet by Canadians is greater than 12.7 hours.

b. Do not reject H₀. We do not have convincing evidence that the mean weekly time spent using the Internet by Canadians is greater than 12.7 hours.     

c. Do not reject H₀. We have convincing evidence that the mean weekly time spent using the Internet by Canadians is greater than 12.7 hours.

d. Reject H₀. We do not have convincing evidence that the mean weekly time spent using the Internet by Canadians is greater than 12.7 hours.

(b) Now suppose that the sample standard deviation was 2 hours. Carry out a hypothesis test with a significance level of 0.05 to decide if there is convincing evidence that the mean time spent using the Internet by Canadians is greater than 12.7 hours. (Use a statistical computer package to calculate the P-value. Round your test statistic to two decimal places and your P-value to three decimal places.)

t= P-value =

State the conclusion in the problem context.

a. Reject H₀. We have convincing evidence that the mean weekly time spent using the Internet by Canadians is greater than 12.7 hours.

b. Do not reject H₀. We do not have convincing evidence that the mean weekly time spent using the Internet by Canadians is greater than 12.7 hours.    

c. Reject H₀. We do not have convincing evidence that the mean weekly time spent using the Internet by Canadians is greater than 12.7 hours.

d. Do not reject H₀. We have convincing evidence that the mean weekly time spent using the Internet by Canadians is greater than 12.7 hours.

(c) Explain why the hypothesis tests resulted in different conclusions for part (a) and part (b).

a.The larger standard deviation means that you can expect less variability in measurements and smaller deviations from the mean. This explains why H₀ is rejected when the sample standard deviation is 6, but not when the sample standard deviation is 2.

b. The smaller standard deviation means that you can expect more variability in measurements and greater deviations from the mean. This explains why H₀ is rejected when the sample standard deviation is 2, but not when the sample standard deviation is 6.     

c. The smaller standard deviation means that you can expect less variability in measurements and smaller deviations from the mean. This explains why H₀ is rejected when the sample standard deviation is 6, but not when the sample standard deviation is 2.

d. The larger standard deviation means that you can expect more variability in measurements and greater deviations from the mean. This explains why H₀ is rejected when the sample standard deviation is 2, but not when the sample standard deviation is 6.

1. A basketball player makes 54% of his shots during the regular season games.
a) To simulate whether a shot hits or misses you could assign random digits as
follows:
(i) One digit simulates one shot; 1 and 5 are a make, other digits are a miss.
(ii) One digit simulates one shot; odd digits are a make and even digits are a miss.
(iii) Two digits simulate one shot; 00 to 54 are a make and 55 to 99 are a miss.
(iv) Two digits simulate one shot; 00 to 53 are a make and 54 to 99 are a miss.
(v) Two digits simulate one shot; 01 to 54 are a make and 55 to 99 are a miss.

b) Using your choice in part (a) and these random digits below, simulate 10 shots.
12734 75390 20867 27513

c) Compute estimated probability:

Toyota’s marketing department is in the process of creating an ad meant to highlight the fuel efficiency of its Camry model compared to its Avalon model. Toyota knows that based on their production process, the miles per gallon (mpg) of both the Camry and the Avalon follow a normal distribution with the Camry having a standard deviation of 1.5 mpg and the Avalon having a standard deviation of 3.6 mpg. Toyota takes a sample of 50 Camry models and 60 Avalon models and finds that the Camry has a mean mpg of 31 while the Avalon has a mean mpg of 29.5 mpg. Toyota would like to know if there is sufficient evidence, at the alpha=0.01 level, to conclude that the Camry has a higher mpg than the Avalon. Answer the following questions.

1. What are the null and alternative hypotheses?

2. What is the critical value?

3. What is the test statistic?

4. What is the probability that you will find the Camry has a higher mpg but really it does not?

5. Will you reject or fail to reject the null hypothesis?

Companies who design furniture for elementary school classrooms produce a variety of sizes for kids of different ages. Suppose the heights of kindergarten children can be described by a Normal model with a mean of 39.2

inches and standard deviation of

1.9inches.

​a) What fraction of kindergarten kids should the company expect to be less than

33 inches​ tall?About blank ​% of kindergarten kids are expected to be less than 33 inches tall.

​(Round to one decimal place as​ needed.)

​b) In what height interval should the company expect to find the middle 80​% of​ kindergarteners?The middle 80​% of kindergarteners are expected to be between what inches and what inches.

​(Use ascending order. Round to one decimal place as​ needed.)

​c) At least how tall are the biggest 30​% of​ kindergarteners?The biggest 30​% of kindergarteners are expected to be at least ? inches tall.

​(Round to one decimal place as​ needed.)

Calculate confidence intervals for ratio of two population variances and ratio of standard deviations. Assume that samples are simple random samples and taken from normal populations.

a. ?=0.05, ?1=30,?1=16.37,?2=39,?2=9.88,

b. ?=0.01, ?1=25,?1=5.2,?2=20,?2=6.8,

4. The Federal Reserve reports that the mean lifespan of a five dollar bill is 4.9 years. Let’s suppose that the standard deviation is 1.9 years and that the distribution of lifespans is normal (not unreasonable!) Find: (a) the probability that a $5 bill will last more than 4 years. (b) the probability that a $5 bill will last between 3 and 5 years. (c) the 97th percentile for the lifespan of these bills (a time such that 97% of bills last less than that time). (d ) the probability that a random sample of 37 bills has a mean lifespan of more than 4.5 years.

A study was conducted to determine the proportion of people who dream in black and white instead of color. Among

306

people over the age of​ 55,

67

dream in black and​ white, and among

287

people under the age of​ 25,

14

dream in black and white. Use a

.05

significance level to test the claim that the proportion of people over 55 who dream in black and white is greater than the proportion for those under 25. Complete parts​ (a) through​ (c) below.

a. Test the claim using a hypothesis test.

Consider the first sample to be the sample of people over the age of 55 and the second sample to be the sample of people under the age of 25. What are the null and alternative hypotheses for the hypothesis​ test?

A.

Upper H 0H0​:

p 1p1equals=p 2p2

Upper H 1H1​:

p 1p1not equals≠p 2p2

B.

Upper H 0H0​:

p 1p1greater than or equals≥p 2p2

Upper H 1H1​:

p 1p1not equals≠p 2p2

C.

Upper H 0H0​:

p 1p1equals=p 2p2

Upper H 1H1​:

p 1p1greater than>p 2p2

D.

Upper H 0H0​:

p 1p1less than or equals≤p 2p2

Upper H 1H1​:

p 1p1not equals≠p 2p2

E.

Upper H 0H0​:

p 1p1not equals≠p 2p2

Upper H 1H1​:

p 1p1equals=p 2p2

F.

Upper H 0H0​:

p 1p1equals=p 2p2

Upper H 1H1​:

p 1p1less than<p 2p2

Identify the test statistic.

zequals=nothing

​(Round to two decimal places as​ needed.)

Identify the​ P-value.

​P-valueequals=nothing

​(Round to three decimal places as​ needed.)

What is the conclusion based on the hypothesis​ test?

The​ P-value is

▼

less than

greater than

the significance level of

alphaαequals=0.050.05​,

so

▼

fail to reject

reject

the null hypothesis. There is

▼

sufficient

insufficient

evidence to support the claim that the proportion of people over 55 who dream in black and white is greater than the proportion for those under 25.

        More

The data set below contains 100 records of heights and weights for some current and recent Major League Baseball (MLB) players.

Note: BMI 18.5 - 24.9 normal group, 25 - 29.9 overweight group and > 30 obese group. 

Compute the body mass index (BMI) (703 times weight in pounds, divided by the square of the height in inches) of each major league baseball player

height Weight(pounds) Age
70 195 25
74 180 23
74 215 35
72 210 31
72 210 35
73 188 36
69 176 29
69 209 31
71 200 35
76 231 30
71 180 27
73 188 24
73 180 27
74 185 23
74 160 26
69 180 28
70 185 34
72 197 30
73 189 28
75 185 22
78 219 23
79 230 26
76 205 36
74 230 31
76 195 32
72 180 31
71 192 29
75 225 29
77 203 32
74 195 36
73 182 26
74 188 27
78 200 24
73 180 27
75 200 25
73 200 28
75 245 30
75 240 31
74 215 31
69 185 32
71 175 28
74 199 28
73 200 29
73 215 24
76 200 22
74 205 25
74 206 27
70 186 33
72 188 31
77 220 33
74 210 33
70 195 31
76 244 37
75 195 26
73 200 23
75 200 25
76 212 24
76 224 35
78 210 27
74 205 31
74 220 28
76 195 30
77 200 25
81 260 24
78 228 30
75 270 26
77 200 23
75 210 26
76 190 25
74 220 32
72 180 24
72 205 25
75 210 24
73 220 24
73 211 32
73 200 30
70 180 24
70 190 32
70 170 23
76 230 27
68 155 26
71 185 26
72 185 28
75 200 25
75 225 33
75 225 35
75 220 31
68 160 29
74 205 29
78 235 28
71 250 34
73 210 31
76 190 38
74 160 24
74 200 26
79 205 24
75 222 24
73 195 28
76 205 33
74 220 36

assume that the MMPI Schizophrenia scale scores are normally distrbuted with mean of 50 and standard deviation of 10. what is the MMPI score at each of the following ranks(that is,precentages of individuals who score MMPI scores)

a. the MMPI score at the 90th precentile rank

b. the MMPI score at the 22th precentile rank

c. the MMPI score at the 50th precentile rank

Find the following probability for the standard normal random variable z. a. ​P(zequals3​) e. ​P(minus3less than or equalszless than or equals3​) b. ​P(zless than or equals3​) f. ​P(minus1less than or equalszless than or equals1​) c. ​P(zless than3​) g. ​P(negative 2.66less than or equalszless than or equals0.06​) d. ​P(zgreater than3​) h. ​P(negative 0.75less thanzless than1.09​)

Let's assume that the average length of all commercials aired on Hulu is 78 seconds. From a sample of 46 commercials aired during sitcoms, it was found that the average length of those commercials was 76 seconds with a standard deviation of 6.1 seconds. At the 5% significance level, does this data provide sufficient evidence to conclude that the mean length of sitcom commercials is different from 78 seconds?

Step 1: Stating what we are testing Step 2: Stating H₀, H_a, and alpha (α) Step 3: Stating the assumptions of the procedureStep 4: Stating whether we are using a z or t procedure and why

Step 5: Providing calculator output (make sure to include all the numbers mentioned in the template in the notes) Step 6: Interpreting results

Step 7: Stating what type of error we would be making and what it means Step 8: Stating the power of the test

a) Plot the histogram, frequency polygon and cumulative frequency polygon.

b) Compute the sample mean, sample variance and sample standard deviation

c) estimate the median from cumulative frequency distribution and mode from the histogram.

d) is this distribution symmetrical or skewed?

e) What percent of the student course load is expected to fall with in 3 standard deviations from the mean?