{"id":33837,"date":"2018-02-20T23:50:30","date_gmt":"2018-02-20T23:50:30","guid":{"rendered":"https:\/\/writemyessayfree.com\/stats-2"},"modified":"2017-08-16T06:21:41","modified_gmt":"2017-08-16T06:21:41","slug":"stats-2","status":"publish","type":"post","link":"https:\/\/www.benedictsol.com\/blogs\/stats-2\/","title":{"rendered":"Stats"},"content":{"rendered":"
\n

Stats<\/p>\n

Information<\/p>\n

The following applies to Questions 1 to 3.<\/p>\n

A box contains four numbered balls (1, 1, 2, and 3). We will randomly select two balls from the box (without replacement).<\/p>\n

(Hint: since the selections are without replacement, this means, for example, that if the ball labelled \u201c2\u201d is selected on the first selection, it can not be selected again on the second selection.<\/p>\n

Question 1 (1 point)<\/p>\n

Description: uestion 1 Saved<\/p>\n

The outcome of interest is the number on each of the two balls we select. How many outcomes are contained in the sample space?<\/p>\n

Your Answer:<\/p>\n

Question 1 options:<\/p>\n

Answer<\/p>\n

Save<\/p>\n

Question 2 (2 points)<\/p>\n

Description: uestion 2 Saved<\/p>\n

Let X be the sum of the two numbers on the selected balls. Find the probability distribution of X.<\/p>\n

In the following four blanks, enter your answers as fractions in the following order: P(X = 2), P(X = 3), P(X = 4), and P(X = 5).<\/p>\n

Question 2 options:<\/p>\n

Blank # 1<\/p>\n

Description: pell check<\/p>\n

Blank # 2<\/p>\n

Description: pell check<\/p>\n

Blank # 3<\/p>\n

Description: pell check<\/p>\n

Blank # 4<\/p>\n

Description: pell check<\/p>\n

Save<\/p>\n

Question 3 (2 points)<\/p>\n

Description: uestion 3 Saved<\/p>\n

What is the probability that X = 3 if we know that the first selection is not a \u201c3\u201d?<\/p>\n

Enter your answer as a fraction.<\/p>\n

Question 3 options:<\/p>\n

Description: pell check<\/p>\n

Save<\/p>\n

Information<\/p>\n

The following applies to Questions 4 to 6.<\/p>\n

A survey of the members of a magazine club revealed the following results:<\/p>\n

\u00b7 42% read Reader\u2019s Digest<\/p>\n

\u00b7 31% read Maclean\u2019s<\/p>\n

\u00b7 50% read Maclean\u2019s or Canadian Geographic<\/p>\n

\u00b7 10% read Reader\u2019s Digest and Canadian Geographic<\/p>\n

\u00b7 9% read Maclean\u2019s and Canadian Geographic<\/p>\n

\u00b7 6% read Reader\u2019s Digest and Maclean\u2019s<\/p>\n

\u00b7 4% read all three magazines<\/p>\n

We will randomly select one member of the magazine club.<\/p>\n

Question 4 (1 point)<\/p>\n

Description: uestion 4 Saved<\/p>\n

What is the probability that the selected person reads Canadian Geographic?<\/p>\n

Enter your answer as a decimal.<\/p>\n

Your Answer:<\/p>\n

Question 4 options:<\/p>\n

Answer<\/p>\n

Save<\/p>\n

Question 5 (1 point)<\/p>\n

Description: uestion 5 Saved<\/p>\n

What is the probability that the selected person reads Maclean\u2019s if we know they don\u2019t read Reader\u2019s Digest?<\/p>\n

Enter your answer as a decimal.<\/p>\n

Your Answer:<\/p>\n

Question 5 options:<\/p>\n

Answer<\/p>\n

Save<\/p>\n

Question 6 (1 point)<\/p>\n

Description: uestion 6 Saved<\/p>\n

What is the probability that the selected person reads Maclean\u2019s if we know they read Reader\u2019s Digest and Canadian Geographic?<\/p>\n

Enter your answer as a decimal.<\/p>\n

Your Answer:<\/p>\n

Question 6 options:<\/p>\n

Answer<\/p>\n

Save<\/p>\n

Information<\/p>\n

The following information about a deck of cards applies to Questions 7 and 8.<\/p>\n

A standard deck of cards consists of 52 cards. There are 13 cards (2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King, Ace) in each of four suits (Clubs, Diamonds, Hearts, and Spades).<\/p>\n

Question 7 (1 point)<\/p>\n

Description: uestion 7 Unsaved<\/p>\n

You randomly select 3 cards without replacement. Let S1 be the event that the first card is a spade, let S2 be the event that the second card is a spade, and let S3 be the event that the third card is a spade. What is PS3(Sc1 Intersection Sc2)?<\/p>\n

Enter your answer as a fraction.<\/p>\n

Question 7 options:<\/p>\n

Description: pell check<\/p>\n

Save<\/p>\n

Question 8 (1 point)<\/p>\n

Description: uestion 8 Unsaved<\/p>\n

You randomly select one card from a deck of cards. Let A be the event that the selected card is an Ace and let H be the event that the selected card is a heart. Are the events A and H independent? Explain why or why not.<\/p>\n

Question 8 options:<\/p>\n

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Save<\/p>\n

Information<\/p>\n

The following applies to Questions 9 and 10.<\/p>\n

Let the probability distribution of X be given as follows:<\/p>\n

xi<\/p>\n

1<\/p>\n

2<\/p>\n

3<\/p>\n

pi<\/p>\n

0.2<\/p>\n

0.3<\/p>\n

0.5<\/p>\n

Question 9 (1 point)<\/p>\n

Description: uestion 9 Unsaved<\/p>\n

What is the expected value of X?<\/p>\n

Enter your answer as a decimal.<\/p>\n

Your Answer:<\/p>\n

Question 9 options:<\/p>\n

Answer<\/p>\n

Save<\/p>\n

Question 10 (1 point)<\/p>\n

Description: uestion 10 Unsaved<\/p>\n

What is the variance of X?<\/p>\n

Keep all decimal places in intermediate calculations and enter your answer as a decimal.<\/p>\n

Your Answer:<\/p>\n

Question 10 options:<\/p>\n

Answer<\/p>\n

Save<\/p>\n

Question 11 (2 points)<\/p>\n

Description: uestion 11 Unsaved<\/p>\n

Scores on the Math portion of a college entrance exam are normally distributed with mean 530 and standard deviation 70. Scores on the Verbal portion of the same exam are normally distributed with mean 475 and standard deviation 75. What is the probability that a randomly selected Math score is greater than a randomly selected Verbal score?<\/p>\n

Your Answer:<\/p>\n

Question 11 options:<\/p>\n

Answer<\/p>\n

Save<\/p>\n

Question 12 (2 points)<\/p>\n

Description: uestion 12 Unsaved<\/p>\n

Quiz scores in a Statistics class follow a normal distribution mean 70 and standard deviation 10.<\/p>\n

In a random sample of 10 students from the class, what is the probability that at least 1 student has a quiz score above 85?<\/p>\n

(Hint: first find the probability that one randomly selected student has a quiz score above 85. Then use this answer to answer the above question.)<\/p>\n

Give your answer to 4 decimal places.<\/p>\n

Your Answer:<\/p>\n

Question 12 options:<\/p>\n

Answer<\/p>\n

Save<\/p>\n

Question 13 (2 points)<\/p>\n

Description: uestion 13 Unsaved<\/p>\n

Trees are distributed in a large forest according to a Poisson distribution with a rate of 0.2 per square meter. If we randomly select a circular area of the forest with a radius of 3 meters, what is the probability this area will contain 5 trees? (Area of a circle = pr2{\u201cversion\u201d:\u201d1.1\u2033,\u201dmath\u201d:\u201dpi r^2\u2033})<\/p>\n

Give your answer to 4 decimal places.<\/p>\n

Your Answer:<\/p>\n

Question 13 options:<\/p>\n

Answer<\/p>\n

Save<\/p>\n

Question 14 (1.5 points)<\/p>\n

Description: uestion 14 Unsaved<\/p>\n

We would like to conduct a hypothesis test at the 10% level of significance to determine if the true proportion of Canadians who are left-handed differs from 0.10. A random sample of 200 Canadians is selected. What is the rejection rule in terms of p\u00cc\u201a {\u201cversion\u201d:\u201d1.1\u2033,\u201dmath\u201d:\u201dhat{p}\u201d}?<\/p>\n

(You do not need to show your work. Just give the final answer. You can write p\u00cc\u201a {\u201cversion\u201d:\u201d1.1\u2033,\u201dmath\u201d:\u201dhat{p}\u201d} as \u201cp-hat\u201d to avoid using the Graphical Equation Editor.)<\/p>\n

Question 14 options:<\/p>\n

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Question 15 (2 points)<\/p>\n

Description: uestion 15 Unsaved<\/p>\n

Question 15 options:<\/p>\n

We would like to compare the current unemployment rates in Canada and the U.S. In a random sample of 400 Canadians, 28 of them are found to be unemployed. In a random sample of 300 Americans, 15 are unemployed. Calculate a 94% confidence interval for the true difference in proportions of Canadian and American adults that are unemployed (pC \u2013 pA).<\/p>\n

Keep 6 decimal places in intermediate calculations and report your final answer to 3 decimal places.<\/p>\n

Lower limit:<\/p>\n

Description: pell check<\/p>\n

Upper limit:<\/p>\n

Description: pell check<\/p>\n

Save<\/p>\n

Information<\/p>\n

The following applies to Questions 16 \u2013 19.<\/p>\n

We would like to compare the grade distributions for three different science courses at a large university. Random samples are selected from first-year biology, chemistry, and physics courses and their final grades are summarized in the table below, as well as some expected cell counts and some cell chi-square values:<\/p>\n

Observed<\/p>\n

Expected<\/p>\n

Cell Chi-Square<\/p>\n

Biology<\/p>\n

Chemistry<\/p>\n

Physics<\/p>\n

Row<\/p>\n

Total<\/p>\n

A+<\/p>\n

17<\/p>\n

20.9<\/p>\n

0.72<\/p>\n

25<\/p>\n

20.3<\/p>\n

1.09<\/p>\n

18<\/p>\n

18.8<\/p>\n

0.04<\/p>\n

60<\/p>\n

A<\/p>\n

32<\/p>\n

24.0<\/p>\n

2.66<\/p>\n

22<\/p>\n

23.3<\/p>\n

0.08<\/p>\n

15<\/p>\n

21.6<\/p>\n

2.04<\/p>\n

69<\/p>\n

B+<\/p>\n

24<\/p>\n

20.5<\/p>\n

0.59<\/p>\n

18<\/p>\n

20.0<\/p>\n

0.19<\/p>\n

17<\/p>\n

18.5<\/p>\n

0.12<\/p>\n

59<\/p>\n

B<\/p>\n

38<\/p>\n

32.0<\/p>\n

1.12<\/p>\n

28<\/p>\n

31.1<\/p>\n

0.32<\/p>\n

26<\/p>\n

28.9<\/p>\n

0.28<\/p>\n

92<\/p>\n

C+<\/p>\n

18<\/p>\n

19.8<\/p>\n

0.17<\/p>\n

20<\/p>\n

19.3<\/p>\n

0.03<\/p>\n

19<\/p>\n

17.9<\/p>\n

0.07<\/p>\n

57<\/p>\n

C<\/p>\n

31<\/p>\n

33.4<\/p>\n

0.17<\/p>\n

34<\/p>\n

32.5<\/p>\n

0.07<\/p>\n

31<\/p>\n

30.1<\/p>\n

0.03<\/p>\n

96<\/p>\n

D<\/p>\n

16<\/p>\n

18.8<\/p>\n

0.41<\/p>\n

17<\/p>\n

18.3<\/p>\n

0.09<\/p>\n

21<\/p>\n

16.9<\/p>\n

0.97<\/p>\n

54<\/p>\n

F<\/p>\n

7<\/p>\n

13.6<\/p>\n

3.18<\/p>\n

14<\/p>\n

13.2<\/p>\n

0.05<\/p>\n

18<\/p>\n

???<\/p>\n

???<\/p>\n

39<\/p>\n

Column Total<\/p>\n

183<\/p>\n

178<\/p>\n

165<\/p>\n

526<\/p>\n

Question 16 (1 point)<\/p>\n

Description: uestion 16 Unsaved<\/p>\n

What are the appropriate hypotheses to test?<\/p>\n

Question 16 options:<\/p>\n

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Question 17 (1 point)<\/p>\n

Description: uestion 17 Saved<\/p>\n

What is the decision rule for testing the hypotheses in Question 16 using the critical value method with a 1% level of significance?<\/p>\n

(The answer is partially pre-filled. Add to the answer.)<\/p>\n

Question 17 options:<\/p>\n

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Question 18 (1 point)<\/p>\n

Description: uestion 18 Unsaved<\/p>\n

What is the appropriate test statistic?<\/p>\n

(To save you time, the sum of the 23 cell chi-square values that are given (excluding the one missing value) is 14.49.)<\/p>\n

Give your answer to 2 decimal places.<\/p>\n

Your Answer:<\/p>\n

Question 18 options:<\/p>\n

Answer<\/p>\n

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Question 19 (1 point)<\/p>\n

Description: uestion 19 Saved<\/p>\n

What is the conclusion of the hypothesis test at the 5% level of significance?<\/p>\n

(The answer is partially pre-filled. Edit\/add to the answer.)<\/p>\n

Question 19 options:<\/p>\n

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The following applies to Questions 20 and 21.<\/p>\n

Three contestants compete on each episode of the TV game show Jeopardy!. The number of female contestants for a random sample of 100 episodes are shown in the table below:<\/p>\n

# of females<\/p>\n

0<\/p>\n

1<\/p>\n

2<\/p>\n

3<\/p>\n

# of episodes<\/p>\n

45<\/p>\n

35<\/p>\n

15<\/p>\n

5<\/p>\n

Question 20 (4 points)<\/p>\n

Description: uestion 20 Saved<\/p>\n

Conduct a chi-square goodness of fit test at the 5% level of significance to determine whether the number of female contestants per episode follows a binomial distribution with parameter p = 0.25.<\/p>\n

Show all of your work. The conclusion of the hypothesis test is partially pre-filled. Edit\/add to the answer.<\/p>\n

Question 20 options:<\/p>\n

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Question 21 (1 point)<\/p>\n

Description: uestion 21 Unsaved<\/p>\n

What would be the estimated value of the parameter p if we didn\u2019t want to make an assumption about its value?<\/p>\n

Give your answer to 2 decimal places.<\/p>\n

Your Answer:<\/p>\n

Question 21 options:<\/p>\n

Answer<\/p>\n

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Stats Information The following applies to Questions 1 to 3. A box contains four numbered balls (1, 1, 2, and 3). We will randomly select two balls from the box (without replacement). (Hint: since the selections are without replacement, this Read More …<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[],"tags":[],"class_list":["post-33837","post","type-post","status-publish","format-standard","hentry"],"_links":{"self":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/posts\/33837","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/comments?post=33837"}],"version-history":[{"count":0,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/posts\/33837\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/media?parent=33837"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/categories?post=33837"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/tags?post=33837"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}