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**Question 1**

Indicate whether the statement is True or False

1. Football jersey numbers are quantitative data-FALSE the numbers are used to identify the players position in the field.

2. There are 107 that are 7-digits long- FALSE since there are restrictions on the 7 digit combinations that form phone numbers. For example, the first digit can’t be 1, that indicates a long distance number.

3. The means of means is not the same as the original mean-TRUE

4. TRUE- The formula for obtaining the upper and lower bounds of the confidence interval by adding and subtracting the margin of error from the mean

5. FALSE a survey of how many children do you have would result in a normal distribution.

6. TRUE-A survey of the question do you have children will result in a binomial distribution because there can only be two outcomes; Yes or No.

7. FALSE-A larger sample size decreases the margin of error

8. TRUE- Parameters are numbers that summarize data for an entire population. Statistics are numbers that summarize data from a sample

9. TRUE-The points scored in a baseball game are discrete data

10. FALSE- A right-skewed distribution will have the mean to the right of the median.

11. FALSE-Association does not imply causation

12. TRUE-The probability of an event happening and the complement of that event should b equal to one.

**Question 2**

1. A

Since the results of the survey have a 4% chance (p=0.04) which is less than the significant level (0.05) we reject the null hypothesis.

2. A

A comparison bar graph would be most appropriate

3. C

The probability of picking up a club is 13/52, since each deck contains 13 club (1♣, 2♣, 3♣, 4♣, 5♣, 6♣, 7♣, 8♣, 9♣, 10♣, J♣, Q♣, K♣) cards.

4. B

There are four Aces in the entire deck; hence, the probability of choosing an ACE is 4/52

5. D

The probability of the first Ace is 4/52 and the second Ace is 3/51; P(A and B)=(4/52*3/51)

6. A

The Z score is the number of standard deviations a data is above or below the mean

7. D

8. C

9. A

10. C

11. C

12. B

The middle value for the data when arranged in ascending order is 1

13. A

The mode is the most frequent value in the data

14. F

15. E

16. E

Thee mean is the central value in the distribution

17. B

It represents the spread, or the difference between one value and another

18. The law of large numbers stats that if one repeats an experiment independently, a large number of times and average results, what one would obtain finally is the expected value. For instance, when you flip a fair coin a number of times, the probability of getting a head h will be a half.

19. This information is not sufficient to conclude that flu shot causes seniors to be hospitalized less often. This is just a statistic, which is not backed using factual evidence. To come to such a conclusion, a hypothesis test would need to be conducted.

20. The graph does not relay the information correctly. Just because the Dem bar is six times higher, we cannot conclude that it was three times the number of republicans. I would use the count instead of percentage to draw thee graph more accurately.

21. A) A statistic that is not normally distributed is the distribution of household income in a high end estate, Most people would be on the higher income side.

b)

22. A) Fail to reject the null hypothesis

Since the standard deviation is known, we use the Z score to test the hypothesis.

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho: μ=72

Ha: μ>72

This corresponds to a right-tailed test, for which a z-test for one mean, with known population standard deviation will be used.

(2) Rejection Region

Based on the information provided, the significance level is α=0.01, and the critical value for a right-tailed test is 2.33z

(3) Test Statistics

The z-statistic is computed as follows:

(4) Decision about the null hypothesis

Since it is observed that z = 1.944 < 2.33, it is then concluded that the null hypothesis is not rejected.

(5) Conclusion

It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that the population mean is greater than 72, at the 0.01 significance level.

B) We do not reject the null hypothesis because there is insufficient evidence to show that the man is greater than 72.

23. a)

b)Without repeats, there would be 10*9*8*7=5040

c)With repeats, there would be 10000-5040=4960 Pins

24. The sample size n;

Therefore, the minimum required sample size is n=728

25. 18C2=153

26. The probability that the first person has an IQ of 150 and above

b)

c) Pat A is not unusual because the probability of it occurring is within four standard deviations of the mean while part b is not within four standard deviations of the mean.

27. A)

B)

C) Normal approximation of the binomial formula

e) I think the probability is much smaller because the sample size has a significant impact on the margin of error.

f)If a coin is flipped 10 times and it comes up tails 6 times, then I would conclude that p=0.5. Ten times is not sufficient to conclude that the alternative hypothesis is true.

II)If it is flipped a hundred times, I would reject the null hypothesis and conclude that p is likely to greater than 0.5 based on the law of large numbers.

28. A) Based on the diagram, it can be seen that the bar is skewed to the right.

B)

x | 0 | 1 | 2 | 3 | 4 |

P(x) | 0.32 | 0.36 | 0.24 | 0.06 | 0.02 |

C) Adding the row up gives 0.32+0.36+0.24+0.06+0.02=1

D) The mean = summation of= (0*0.32)+(1*0.36)+(2*0.24)+(3*0.06)+(4*0.02)=1.1

E) The margin of error for the survey will be; (2.724*0.7/sqrt36)=0.3178

F) Based on the results of the survey, we are 99% confident that the population means M is between 0.9822 and 1.6178

G) Yes, the survey got it right. The true value of M=1.1 is contained in the above interval.

H) The best way to increase precision, would be to increase the sample size since that would increase sampling precision

Bonus +1: In general, the degrees of freedom of an estimate of a parameter are equal to the number of independent scores that go into the estimate minus the number of parameters used as intermediate steps in the estimation of the parameter itself. Therefore, the sample variance has n-1 degrees of freedom, since it is computed from n random scores minus the only 1 parameter estimated as intermediate step, which is the sample mean.

Bonus +6:

a) In the courtroom, rejecting the null hypothesis when it is actually true means that, rejecting the claim that a defendant is innocent when they are innocent in deed. A type II error would occur when the courtroom decides that the defendant is innocent when in fact they are guilty.

b) The error that the justice system tries to avoid is the probability of a type II error since it is more costly, can have worse consequences.

c) In my opinion, a type II error would be more dangerous to make since the effects of setting free crime offenders such as murderers, pedophiles and rapists would be much worse.

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