(a). A simple random sample of 37 days was selected. For these 37 days, Parsnip was fed seeds on 22 days and Parsnip was fed pellets on the other 15 days. The goal is to calculate a 99% confidence interval for the proportion of all days in which Parsnip was fed seeds, and to do so there are two assumptions. The first is that there is a simple random sample, which is satisfied. What is the second assumption, and specific to the information in this problem, is it satisfied? Explain why or why not.

(b). If appropriate, use the data in part (a) to calculate and interpret a 99% confidence interval for the proportion of all days in his life that Parsnip has been fed seeds.

In: Statistics and Probability

You are raising money for a charity and know that the average donation is $50 with a standard deviation of $60. Suppose you collect donations from 400 independent individuals. Use the Central Limit Theorem to construct X, a normal approximation to the total amount of money collected.

(a) What is E(X) and σX?

(b) What is the CDF of X in terms of the Φ function?

(c) What is the probability that you raise more than $22,000?

(d) What is the probability that you raise between $19,000 and $21,000? (e) What is the probability that X is within 2.58 standard deviations from the mean?

In: Statistics and Probability

The following data was drawn from an industry, there were 12 machine's working hours and number of units they could produce was tabulated as follows,

Hours (X) | 80 | 79 | 83 | 84 | 78 | 60 | 82 | 85 | 79 | 84 | 80 | 62 |

Production(Y) | 300 | 302 | 315 | 330 | 300 | 250 | 300 | 340 | 315 | 330 | 310 | 240 |

a) The management wish to know that the relation between working hours and their corresponding output is in a benefited way. Justify you answer with the management's hypothesis. Apply correlation coefficient formula for testing the hyposthesis.

b) Using appropriate software, you are asked to summarise the above statistical data you have been investigating in a method that can be understood by non-technical colleagues.

In: Statistics and Probability

Suppose you are ordering pizza from a restaurant that is known to complete one order every 10 minutes. Let N be a Poisson RV modeling the number of orders completed in an hour.

(a) What is Λ?

(b) What is the probability that fewer than (or equal to) 5 orders are completed in one hour?

(c) What is the probability that between (or including) 4 to 8 orders are completed in an hour?

(d) What is the probability that more than (or equal to) 7 orders are completed in one hour?

In: Statistics and Probability

Suppose you are testing products for defects and find that one in every 17 products exhibits a defect. Let T be the geometric RV modeling the number of products tested until a defect is found.

(a) What is the parameter q for T?

(b) Compute the probability that the first product tested exhibits a defect.

(c) Compute the probability that the first defective product is one of the first 10 tested.

(d) Compute the probability that the first defective product is not found until 8 or more products are tested.

In: Statistics and Probability

Consider two independent experiments testing for two different and independent genetic mutations in rabbits. •

•Experiment A: Tests 12 rabbits for a mutation that occurs with probability 0.1. Let X be the number of these rabbits w/ this mutation.

• Experiment B: Tests 16 rabbits for a mutation that occurs with probability 0.25. Let Y be the number of these rabbits w/ this mutation.

(a) Compute P(X ≤ 6)

(b) Compute P(10 ≤ Y ).

(c) Compute the joint probability P(X = 4, Y = 6).

(d) Compute the joint probability P(X ≤ 3 and Y ≤ 4).

In: Statistics and Probability

**One card is selected from a deck of cards. Find the
probability of selecting a diamond or a card less than 7. (Round
answer to four decimals.)**

In: Statistics and Probability

Suppose that there is a class of n students. Homework is to be returned to students, but the students’ homework assignments have been shuffled and are distributed at random to students.

a) Calculate the probability that you get your own homework back. (I think it is 1/n)

b) Suppose that I tell you that another student, Betty, got her own homework. Does this change the probability that you get your own homework, and if so what is the new probability? (I think it is now 1/(n-1)

c) What is the expected number of students who receive their own homework?

d) Find an approximation for the distribution of the random variable denoting the number of students who receive their own homework in the limit of large n.

In: Statistics and Probability

Given the following dataset

x | 1 | 1 | 2 | 3 | 4 | 5 |

y | 0 | 2 | 4 | 5 | 5 | 3 |

We want to test the claim that there is a correlation between xand y.

(a) What is the null hypothesis Ho and the alternative hypothesis H1?

(b) Using α= 0.05, will you reject Ho? Justify your answer by using a p-value.

(c) Base on your answer in part (b), is there evidence to support the claim?

(d) Find r, the linear correlation coefficient.

The level of cretaine phosphokinase (CPK) in blood samples measures the amount of muscle damage for athletes. At Jock State University, the level of CPK was determined for each of 25 football players and 15 soccer players before and after practice. The two groups of athletes are trained independently. The data summary is as follows :For football players :

n=25 | before practice | after practice | difference(before-after) |

mean | 254.73 | 225.6 | 29.13 |

St.deviation | 115.5 | 132.6 | 21.00 |

For soccer players :

n=15 | before practice | after practice | difference(before-after) |

mean | 177.1 | 173.8 | 3.3 |

st.deviation | 60.7 | 64.4 | 6.88 |

Assume that all the data above are normal, use the information above to answer problems 7 to 10.

7. Construct a 95% Confidence Interval for the difference in mean CPK values for foot-ball players and soccer players BEFORE exercises.

8. Construct a 95% Confidence Interval for the difference in mean CPK values for foot-ball players BEFORE and AFTER exercises.

9. Test the claim that the mean CPK level has DECREASED for soccer players AFTERexercise (compared to the mean BEFORE exercise), using α= 0.10.

10. AFTER practice, do football players have a DIFFERENT mean CPK values com-pared to soccer players? Test this claim by performing a hypothesis test, usingα= 0.10.

In: Statistics and Probability

Assuming a random variate follows a binomial distribution with
*x* "successes" in *n* "experiments", and the
probability of a single success in any given experiment being
*p*; compute:

(a) *Pr*(*x*=2, *n*=8, *p*=0.47)

(b) *Pr*(3 < *X* ≤ 5) when *n* = 9 and
*p* = 0.6

(c) *Pr*(*X* ≤ 3) when *n* = 9 and
*p* = 0.13

(d) The probability that the number of successes is more than 1
when *n* = 13 and *p* = 0.19

(e) The uncertainty in the number of successes when *n* =
11 and *p* = 0.14

(f) The mean number of successes when *n* = 10 and
*p* = 0.07

(g) *Pr*(3 ≤ *X* ≤ 5) when *n* = 8 and
*p* = 0.79

In: Statistics and Probability

I want to provide this solution for other students to see.

A university financial aid office polled a random sample of 591 male undergraduate students and 484 female undergraduate students. Each of the students was asked whether or not they were employed during the previous summer. 424424 of the male students and 385 of the female students said that they had worked during the previous summer. Give a 95% confidence interval for the difference between the proportions of male and female students who were employed during the summer. Find the point estimate. Then, the margin of error. Finally, construct the 95% confidence interval. Round your answers to three decimal places.

Explaination: In the previous steps, we determined that the point estimate for the given information is pˆ1−pˆ2=−0.078p^1−p^2=−0.078 and the margin of error is E=0.051113E=0.051113. To determine the confidence interval, we must find the lower endpoint and the upper endpoint, rounding the values to three decimal places.

Lower endpoint: pˆ1−pˆ2−E=−0.078−0.051113≈−0.129Upper endpoint: pˆ1−pˆ2+E=−0.078+0.051113≈−0.027

ANSWERS

Point Estimate = **−0.078**

Margin of Error = **0.051113**

Lower endpoint: **−0.129**, Upper endpoint:
**−0.027**

In: Statistics and Probability

f) Calculate a 90% confidence interval estimate of applying fertilizer B data for crop yield in all plots of lands and interpret your results.

g) Assuming population mean of crop yield is 570 bushels for all fertilizers with standard deviation of 40 bushels for all. Formulate a test hypothesis that crop yield by applying fertilizer C differs from the population crop yield for all fertilizers. Conduct the hypothesis test, conclude your analysis and explain your answer. Use both critical value and p-value approach with alpha=0.05

h) Calculate a 90% confidence interval estimate of the difference between the population mean yield of fertilizers B and A. Can we conclude at 0.05 level of significance, that the crop yield using fertilizer B is greater than the crop yield using fertilizer A? (hint: you can use the template in chapter 10 to calculate degrees of freedom and the standard error)

i) If we assume that observations are now plots of lands, can the scientist infer that there are differences between the three types of fertilizers?

Plot |
Fertilizer A |
Fertilizer B |
Fertilizer C |

1 | 563 | 588 | 575 |

2 | 593 | 624 | 593 |

3 | 542 | 576 | 564 |

4 | 649 | 672 | 653 |

5 | 565 | 583 | 556 |

6 | 587 | 612 | 590 |

7 | 595 | 617 | 607 |

8 | 429 | 446 | 423 |

9 | 500 | 515 | 483 |

10 | 610 | 641 | 626 |

11 | 524 | 547 | 523 |

12 | 559 | 586 | 568 |

13 | 546 | 582 | 551 |

14 | 503 | 530 | 502 |

15 | 550 | 573 | 567 |

16 | 492 | 518 | 495 |

17 | 497 | 529 | 513 |

18 | 619 | 643 | 626 |

19 | 473 | 497 | 479 |

20 | 533 | 556 | 540 |

In: Statistics and Probability

The *One-Way ANOVA* applet lets you see how the
*F* statistic and the *P*-value depend on the
variability of the data within groups, the sample size, and the
differences among the means.

Corporate advertising tries to enhance the image of the
corporation. A study compared two ads from two sources, the
*Wall Street Journal* and the *National Enquirer*.
Subjects were asked to pretend that their company was considering a
major investment in Performax, the fictitious sportswear firm in
the ads. Each subject was asked to respond to the question "How
trustworthy was the source in the sportswear company ad for
Performax?" on a 7-point scale. Higher values indicated more
trustworthiness. Here is a summary of the results.

Ad source | n |
x |
s |
---|---|---|---|

Wall Street Journal |
66 | 4.77 | 1.50 |

National Enquirer |
61 | 2.43 | 1. |

Find the two-sample pooled *t* statistic. Then formulate
the problem as an ANOVA and report the results of this analysis.
Verify that *F* = *t* ^{2}.

In: Statistics and Probability

A study of reading comprehension in children compared three methods of instruction. The three methods of instruction are called Basal, DRTA, and Strategies. Basal is the traditional method of teaching, while DRTA and Strategies are two innovative methods based on similar theoretical considerations. The READING data set includes three response variables that the new methods were designed to improve. Analyze these variables using ANOVA methods. Be sure to include multiple comparisons or contrasts as needed. Write a report summarizing your findings.

Data

subject group pre1 pre2 post1 post2 post3 1 B 4 3 5 4 41 2 B 6 5 9 5 41 3 B 9 4 5 3 43 4 B 12 6 8 5 46 5 B 16 5 10 9 46 6 B 15 13 9 8 45 7 B 14 8 12 5 45 8 B 12 7 5 5 32 9 B 12 3 8 7 33 10 B 8 8 7 7 39 11 B 13 7 12 4 42 12 B 9 2 4 4 45 13 B 12 5 4 6 39 14 B 12 2 8 8 44 15 B 12 2 6 4 36 16 B 10 10 9 10 49 17 B 8 5 3 3 40 18 B 12 5 5 5 35 19 B 11 3 4 5 36 20 B 8 4 2 3 40 21 B 7 3 5 4 54 22 B 9 6 7 8 32 23 D 7 2 7 6 31 24 D 7 6 5 6 40 25 D 12 4 13 3 48 26 D 10 1 5 7 30 27 D 16 8 14 7 42 28 D 15 7 14 6 48 29 D 9 6 10 9 49 30 D 8 7 13 5 53 31 D 13 7 12 7 48 32 D 12 8 11 6 43 33 D 7 6 8 5 55 34 D 6 2 7 0 55 35 D 8 4 10 6 57 36 D 9 6 8 6 53 37 D 9 4 8 7 37 38 D 8 4 10 11 50 39 D 9 5 12 6 54 40 D 13 6 10 6 41 41 D 10 2 11 6 49 42 D 8 6 7 8 47 43 D 8 5 8 8 49 44 D 10 6 12 6 49 45 S 11 7 11 12 53 46 S 7 6 4 8 47 47 S 4 6 4 10 41 48 S 7 2 4 4 49 49 S 7 6 3 9 43 50 S 6 5 8 5 45 51 S 11 5 12 8 50 52 S 14 6 14 12 48 53 S 13 6 12 11 49 54 S 9 5 7 11 42 55 S 12 3 5 10 38 56 S 13 9 9 9 42 57 S 4 6 1 10 34 58 S 13 8 13 1 48 59 S 6 4 7 9 51 60 S 12 3 5 13 33 61 S 6 6 7 9 44 62 S 11 4 11 7 48 63 S 14 4 15 7 49 64 S 8 2 9 5 33 65 S 5 3 6 8 45 66 S 8 3 4 6 42

In: Statistics and Probability

A study of reading comprehension in children compared three methods of instruction. The three methods of instruction are called Basal, DRTA, and Strategies. As is common in such studies, several pretest variables were measured before any instruction was given. One purpose of the pretest was to see if the three groups of children were similar in their comprehension skills. The READING data set described in the Data Appendix gives two pretest measures that were used in this study. Use one-way ANOVA to analyze these data and write a summary of your results.

Reading Data:

subject group pre1 pre2 post1 post2 post3 1 B 4 3 5 4 41 2 B 6 5 9 5 41 3 B 9 4 5 3 43 4 B 12 6 8 5 46 5 B 16 5 10 9 46 6 B 15 13 9 8 45 7 B 14 8 12 5 45 8 B 12 7 5 5 32 9 B 12 3 8 7 33 10 B 8 8 7 7 39 11 B 13 7 12 4 42 12 B 9 2 4 4 45 13 B 12 5 4 6 39 14 B 12 2 8 8 44 15 B 12 2 6 4 36 16 B 10 10 9 10 49 17 B 8 5 3 3 40 18 B 12 5 5 5 35 19 B 11 3 4 5 36 20 B 8 4 2 3 40 21 B 7 3 5 4 54 22 B 9 6 7 8 32 23 D 7 2 7 6 31 24 D 7 6 5 6 40 25 D 12 4 13 3 48 26 D 10 1 5 7 30 27 D 16 8 14 7 42 28 D 15 7 14 6 48 29 D 9 6 10 9 49 30 D 8 7 13 5 53 31 D 13 7 12 7 48 32 D 12 8 11 6 43 33 D 7 6 8 5 55 34 D 6 2 7 0 55 35 D 8 4 10 6 57 36 D 9 6 8 6 53 37 D 9 4 8 7 37 38 D 8 4 10 11 50 39 D 9 5 12 6 54 40 D 13 6 10 6 41 41 D 10 2 11 6 49 42 D 8 6 7 8 47 43 D 8 5 8 8 49 44 D 10 6 12 6 49 45 S 11 7 11 12 53 46 S 7 6 4 8 47 47 S 4 6 4 10 41 48 S 7 2 4 4 49 49 S 7 6 3 9 43 50 S 6 5 8 5 45 51 S 11 5 12 8 50 52 S 14 6 14 12 48 53 S 13 6 12 11 49 54 S 9 5 7 11 42 55 S 12 3 5 10 38 56 S 13 9 9 9 42 57 S 4 6 1 10 34 58 S 13 8 13 1 48 59 S 6 4 7 9 51 60 S 12 3 5 13 33 61 S 6 6 7 9 44 62 S 11 4 11 7 48 63 S 14 4 15 7 49 64 S 8 2 9 5 33 65 S 5 3 6 8 45 66 S 8 3 4 6 42

In: Statistics and Probability