1) The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 35 ounces and a standard deviation of 9 ounces.

Use the Standard Deviation Rule, also known as the Empirical Rule.

Suggestion: sketch the distribution in order to answer these questions.

a) 95% of the widget weights lie betweenand

b) What percentage of the widget weights lie between 26 and 53 ounces?%

c) What percentage of the widget weights lie below 62 ?%

2) Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0C and a standard deviation of 1.00C. A single thermometer is randomly selected and tested. Find the probability of obtaining a reading between -1.453C and -1.252C. Round to 4 decimal places.

P(1.453 < Z < 1.252)=

3) A manufacturer knows that their items have a normally distributed length, with a mean of 13.9 inches, and standard deviation of 2 inches.

If one item is chosen at random, what is the probability that it is less than 9 inches long? Round your answer to 4 decimal places

4) A distribution of values is normal with a mean of 193.2 and a standard deviation of 81.4.

FindP₂₉, which is the score separating the bottom 29% from the top 71%.

P₂₉=

5) Engineers must consider the breadths of male heads when designing helmets. The company researchers have determined that the population of potential clientele have head breadths that are normally distributed with a mean of 6.3-in and a standard deviation of 0.9-in. Due to financial constraints, the helmets will be designed to fit all men except those with head breadths that are in the smallest 2.6% or largest 2.6%.

What is the minimum head breadth that will fit the clientele?

min =

What is the maximum head breadth that will fit the clientele?

max =

Enter your answer as a number accurate to 1 decimal place.

6) The population of weights for men attending a local health club is normally distributed with a mean of 176-lbs and a standard deviation of 28-lbs. An elevator in the health club is limited to 34 occupants, but it will be overloaded if the total weight is in excess of 6460-lbs.

Assume that there are 34 men in the elevator. What is the average weight beyond which the elevator would be considered overloaded?

average weight =lbs

What is the probability that one randomly selected male health club member will exceed this weight?

P(one man exceeds) =

(Report answer accurate to 4 decimal places.)

If we assume that 34 male occupants in the elevator are the result of a random selection, find the probability that the elevator will be overloaded?

P(elevator overloaded) =

(Report answer accurate to 4 decimal places.)

If the elevator is full (on average) 8 times a day, how many times will the elevator be overloaded in one (non-leap) year?

number of times overloaded =

(Report answer rounded to the nearest whole number.)

Is there reason for concern?

A) yes, the current overload limit is not adequate to insure the safey of the passengers

B) no, the current overload limit is adequate to insure the safety of the passengers

7) Out of 200 people sampled, 134 had kids. Based on this, construct a 95% confidence interval for the true population proportion of people with kids.

Give your answers as decimals, to three places

( < p < )

What is the correct interpretation for the confidence interval?

A) With 95% confidence, the true proportion of people with kids will be in the above interval.

B) The true proportion of people with kids is in the above interval, 95% of the time. We know this is true because the proportion of our sample is in the interval

C) There is a 95% chance that the true proportion of people with kids will be in the above interval.

8) You intend to estimate a population mean with a confidence interval. The population standard deviation is unknown. You believe the population to have a normal distribution. Your sample size is 16.

Find the positive critical value that corresponds to a confidence level of 85%.

(Round answer to two decimal places.)

t_a/2=

9) Karen wants to advertise how many chocolate chips are in each Big Chip cookie at her bakery. She randomly selects a sample of 52 cookies and finds that the number of chocolate chips per cookie in the sample has a mean of 18.1 and a standard deviation of 2.4. What is the 80% confidence interval for the number of chocolate chips per cookie for Big Chip cookies? Round your answers to 3 decimal places.

Enter your answers( << )

10) You are conducting a study to see if the proportion of women over 40 who regularly have mammograms is significantly less than 23%. WithH₁: p< 23% you obtain a test statistic ofz=-1.747. Find the p-value accurate to 4 decimal places.

p-value =

11) Test the claim that the proportion of people who own cats is larger than 20% at the 0.05 significance level.

The null and alternative hypothesis would be:

A)H0:0.2; H1:>0.2

B) H0:p=0.2; H1:p0.2

C)H0:p0.2; H1:p<0.2

D) H0:p0.2; H1:p>0.2

E) H0:0.2; H1:<0.2

F) H0:=0.2; H1:0.2

The test is:

A) two-tailed

B) left-tailed

C) right-tailed

Based on a sample of 300 people, 27% owned cats

The test statistic is:(to 2 decimals)

The p-value is:(to 4 decimals)

Based on this we:

A) Reject the null hypothesis

B) Fail to reject the null hypothesis

12) Test the claim that the mean GPA of night students is smaller than 3.2 at the .005 significance level.

The null and alternative hypothesis would be:

A) H0:=3.2; H1:3.2

B) H0:p=0.8; H1:p0.8

C) H0:p=0.8; H1:p>0.8

D) H0:=3.2; H1:<3.2

E) H0:p=0.8; H1:p<0.8

F) H0:=3.2; H1:>3.2

The test is:

A) right-tailed

B) left-tailed

C) two-tailed

Based on a sample of 70 people, the sample mean GPA was 3.17 with a standard deviation of 0.06

The test statistic is:(to 2 decimals)

The critical value is:(to 2 decimals)

Based on this we:

A) Fail to reject the null hypothesis

B) Reject the null hypothesis

13) You wish to test the following claim (H1) at a significance level of=0.02.

H0:=87.4

H1:>87.4

You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of sizen=5 with meanx=107.1 and a standard deviation ofs=18.4.

What is the test statistic for this sample? (Report answer accurate to two decimal places.)

test statistic =

What is the p-value for this sample? (Report answer accurate to four decimal places.)

p-value =

The p-value is...

A) less than (or equal to)

B) greater than

This test statistic leads to a decision to...

A) reject the null

B) accept the null

C) fail to reject the null

As such, the final conclusion is that...

A) There is sufficient evidence to warrant rejection of the claim that the population mean is greater than 87.4.

B) There is not sufficient evidence to warrant rejection of the claim that the population mean is greater than 87.4.

C) The sample data support the claim that the population mean is greater than 87.4.

D) There is not sufficient sample evidence to support the claim that the population mean is greater than 87.4.

14) You wish to test the following claim (H1) at a significance level of=0.005.

Ho:p1=p2

H1:p1p2

You obtain 48% successes in a sample of sizen1=400 from the first population. You obtain 36% successes in a sample of sizen2=400 from the second population.

What is the test statistic for this sample? (Report answer accurate to three decimal places.)

test statistic =

What is the p-value for this sample? (Report answer accurate to four decimal places.)

p-value =

The p-value is...

A) less than (or equal to)

B) greater than

This test statistic leads to a decision to...

A)reject the null

B) accept the null

C) fail to reject the null

As such, the final conclusion is that...

A) There is sufficient evidence to warrant rejection of the claim that the first population proportion is not equal to the second population proportion.

B) There is not sufficient evidence to warrant rejection of the claim that the first population proportion is not equal to the second population proportion.

C) The sample data support the claim that the first population proportion is not equal to the second population proportion.

D) There is not sufficient sample evidence to support the claim that the first population proportion is not equal to the second population proportion.

What is the confidence interval for the difference of the two proportions? (Report answers accurate to two decimal places.)

( < p1p2< )

15) You wish to test the following claim (H1) at a significance level of=0.05.

Ho:1=2

H1:1>2

You believe both populations are normally distributed, but you do not know the standard deviations for either. However, you also have no reason to believe the variances of the two populations are not equal. You obtain a sample of sizen1=14 with a mean ofx1=84.9 and a standard deviation ofs1=20.7 from the first population. You obtain a sample of sizen2=25 with a mean ofx2=78 and a standard deviation ofs2=15.2from the second population.

What is the test statistic for this sample? (Report answer accurate to two decimal places.)

test statistic =

What is the p-value for this sample? (Report answer accurate to four decimal places.)

p-value =

The p-value is...

A) less than (or equal to)

B) greater than

This p-value leads to a decision to...

A) reject the null

B) accept the null

C) fail to reject the null

As such, the final conclusion is that...

A) There is sufficient evidence to warrant rejection of the claim that the first population mean is greater than the second population mean.

B) There is not sufficient evidence to warrant rejection of the claim that the first population mean is greater than the second population mean.

C) The sample data support the claim that the first population mean is greater than the second population mean.

D) There is not sufficient sample evidence to support the claim that the first population mean is greater than the second population mean.

16) You wish to test the following claim (H1) at a significance level of=0.002. For the context of this problem,d=2-1 where the first data set represents a pre-test and the second data set represents a post-test.

Ho:d=0

H1:d>0

You believe the population of difference in scores is normally distributed, but you do not know the standard deviation. You obtain the following sample of data:

pre-test post-test

73.1 103.2

75.7 44.6

67.2 155.9

33.4 163.4

66.5 30.3

38.9 49.1

58.4 129.7

68.6 127.4

42.7 25.3

69.4 130.5

58 146.7

What is the test statistic for this sample? (Report answer accurate to 2 decimal places.)

test statistic =

What is the p-value for this sample? (Report answer accurate to 4 decimal places.)

p-value =

The p-value is...

A) less than (or equal to)

B) greater than

This test statistic leads to a decision to...

A) reject the null

B) accept the null

C) fail to reject the null

As such, the final conclusion is that...

A) There is sufficient evidence to warrant rejection of the claim that the mean difference of post-test from pre-test is greater than 0.

B) There is not sufficient evidence to warrant rejection of the claim that the mean difference of post-test from pre-test is greater than 0.

C) The sample data support the claim that the mean difference of post-test from pre-test is greater than 0.

D) There is not sufficient sample evidence to support the claim that the mean difference of post-test from pre-test is greater than 0.

17) The midterm and final exam scores for a sample of 18 students were recorded. The scores for the 18 students are shown below:

Midterm Exam Score Final Exam Score

55 72

69 80

68 63

53 78

53 62

50 76

63 73

60 69

54 64

82 80

85 86

86 82

76 99

90 93

81 93

82 91

93 89

95 100

Test the claim that there is significant correlation between midterm and final exam scores at the0.05significance level.

a) If we useM to denote the midterm exam scores andFto denote the final exam scores, identify the correct alternative hypothesis.

A) H1:=0

B) H1:0

C) H1:0

D) H1:pMpF

E) H1:r0

b) Thercorrelation coefficient is:(round to 3 decimal places)

c) The critical value is:(round to 3 decimal places)

Use the critical value table below

d) Based on this, we

A) RejectH0

B) Fail to rejectH0

e) Which means

A) The sample data supports the claim

B) There is not sufficient evidence to warrant rejection of the claim

C) There is sufficient evidence to warrant rejection of the claim

D) There is not sufficient evidence to support the claim

f) The regression equation (in terms of incomex) is: y^= (round to 2 decimal places)

g) To predict what score a student will make on the final exam, it would be most appropriate to:

A) Use the regression equation

B) Use the mean final exam score

C) Use the p-Value

D) Use the residual

Degrees of Freedom: n-2 Critical Value: (+ or -)0.05 Significance Level

1 0.997

2 0.95

3 0.878

4 0.811

5 0.754

6 0.707

7 0.666

8 0.632

9 0.602

10 0.576

11 0.553

12 0.532

13 0.514

14 0.497

15 0.482

16 0.468

17 0.456

18 0.444

19 0.433

20 0.423

21 0.413

22 0.404

23 0.396

24 0.388

25 0.381

26 0.374

27 0.367

28 0.361

29 0.355

30 0.349

18) Monthly high temperatures in a certain location have been tracked for several months. LetX represent the month andYthe high temperature (in degrees Fahrenheit). Based on the data shown below, at the 0.05 significance level, is the correlation significant?

x y

3 20.38

4 17.84

5 23.3

6 10.26

7 12.22

8 22.68

9 20.14

10 17.1

11 16.56

12 8.02

13 13.98

14 17.94

15 17.4

A) Yes, significant correlation

B) No, not a significant correlation

You intend to predict the high temperature in month 17 using the sample data. Which of the following is the best prediction:

A) 14.19 degrees

B) 8.24 degrees

C) between 13.84 and 19.67 degrees

D) between 6.53 and 11.47 degrees

19) You are conducting a multinomial Goodness of Fit Hypothesis Test (= 0.05) for the claim that all 5 categories are equally likely to be selected. Complete the table.

Category Observed Frequency Expected Frequency

A 25

B 10

C 15

D 10

E 15

Report all answers to the indicated number of decimal places.

What is the chi-square test-statistic for this data? (Report answer accurate to three decimal places.)

2=

What are the degrees of freedom for this test?

d.f.=

What is the p-value for this sample? (Report answer accurate to four decimal places.)

p-value =

The p-value is...

A) less than (or equal to)

B) greater than

This test statistic leads to a decision to...

A) reject the null

B) accept the null

C) fail to reject the null

D) accept the alternative

As such, the final conclusion is that...

A) There is sufficient evidence to warrant rejection of the claim that all 5 categories are equally likely to be selected.

B) There is not sufficient evidence to warrant rejection of the claim that all 5 categories are equally likely to be selected.

C) The sample data support the claim that all 5 categories are equally likely to be selected.

D) There is not sufficient sample evidence to support the claim that all 5 categories are equally likely to be selected.

20) You are conducting a test of the claim that the row variable and the column variable are dependentin the following contingency table.

X Y Z

A18 62 33

B7 62 26

(a) What is the chi-squaretest-statisticfor this data?

Test Statistic: (round to 3 decimal places)

2=

(b) What is thep-valuefor this test of independence?

p-value: (round to 4 decimal places)

p-value =

(c) What is the correct conclusion of this hypothesis test at the 0.01 significance level?

A) Thereissufficient evidence to warrantrejectionof the claim that the row and column variables are dependent.

B) Thereissufficient evidence tosupportthe claim that the row and column variables are dependent.

C) There isnotsufficient evidence tosupportthe claim that the row and column variables are dependent.

D) There isnotsufficient evidence to warrantrejectionof the claim that the row and column variables are dependent.

PLEASE BREAK DOWN HOW TO WORK THESE PROBLEMS OUT I DO NOT UNDERSTAND HOW TO DO THESE I KEEP GETTING THEM WRONG.