Multiple choice question | Numerical analysis homework help

Question10
The taste test for PTC (phenylthiourea) is a common class demonstration in the study of genetics. It is known that 70% of the American people are “tasters” with the rest are “non-tasters”. Suppose a genetics class of size 20 does the test to see if they match the American percentage of “tasters” and “non-tasters”. Assume that the assignment of students to classes is a random process. Calculate the mean.


3


6


7


14


Question 11
The taste test for PTC (phenylthiourea) is a common class demonstration in the study of genetics. It is known that 70% of the American people are “tasters” with the rest are “non-tasters”. Suppose a genetics class of size 20 does the test to see if they match the American percentage of “tasters” and “non-tasters”. Assume that the assignment of students to classes is a random process. Calculate the variance.


4.2


5.5


8.4


9.3

Question 12
A quiz consists of 18 questions. Each question has 2 answer choices with exactly one correct answer. A student is completely unprepared for the quiz, so he guesses on all 18 questions. How many questions should the student expect to answer correctly?


6


8


9


12


18

Question 13
A quiz consists of 25 questions. Each question has 5 answer choices with exactly one correct answer. A student is completely unprepared for the quiz, so he guesses on all 25 questions. How many questions should the student expect to answer incorrectly?


1


5


10


15


20

Question 14
Car color preferences change over the years and according to the particular model that the customer selects. In a recent year, 20% of all luxury cars sold were white. Assume that 25 cars of that year and type are randomly selected. What is the definition of “success” in this binomial distribution application?


The chosen luxury car is black.


The chosen luxury car is not black.


The chosen luxury car is not white.


The chosen luxury car is white.






Question 15

A medical association study shows that 20% of all Americans suffer from high blood pressure. Suppose that 10 Americans are randomly selected and each person is asked if he has high blood pressure. What is the probability of “success” in a single trial of this binomial distribution application?


10%


20%


50%


80%


90%






Question 16
It is known that 10% of the customers in an electronics store purchase an MP3 player. A random sample of 30 customers is selected. Assume that the customers’ purchases are made independently. In this binomial distribution application, which Excel statement will find the probability of exactly 10 customers who purchase an MP3 player in this electronics store?


=1- BINOMDIST(10,30,10%,TRUE)


=1- BINOMDIST(10,30,10%,FALSE)


=BINOMDIST(10,30,10%,TRUE)


=BINOMDIST(10,30,10%,FALSE)







Question 17
It is known that 10% of the customers in an electronics store purchase an MP3 player. A random sample of 30 customers is selected. Assume that the customers’ purchases are made independently. In this binomial distribution application, which Excel statement will find the probability of 10 or fewer customers who purchase an MP3 player in this electronics store?


=1- BINOMDIST(10,30,10%,TRUE)


=1- BINOMDIST(10,30,10%,FALSE)


=BINOMDIST(10,30,10%,TRUE)


=BINOMDIST(10,30,10%,FALSE)



Question 18
A new surgical procedure is said to be successful 90% of the time. Suppose the procedure is performed five times. Assume that the results of each procedure are independent of one another. In this binomial distribution application, which Excel statement will find the probability of more than 2 successful surgical procedures?


=BINOMDIST(2,5,90%,TRUE)


=BINOMDIST(2,5,90%,FALSE)


=1-BINOMDIST(2,5,90%,TRUE)


=1-BINOMDIST(2,5,90%,FALSE)







Question 19
A new surgical procedure is said to be successful 90% of the time. Suppose the procedure is performed five times. Assume that the results of each procedure are independent of one another. In this binomial distribution application, which Excel statement will find the probability of between 2 and 4, inclusively, successful surgical procedures?


=BINOMDIST(4,5,90%,FALSE)-BINOMDIST(2,5,90%,FALSE)


=BINOMDIST(4,5,90%,TRUE)-BINOMDIST(1,5,90%,TRUE)


=1-BINOMDIST(2,4,5,90%,TRUE)


=1-BINOMDIST(2,4,5,90%,FALSE)







Question 20
Which of the following statement(s) is(are) a characteristic(s) of the normal distribution?
• It is symmetric.
• It has a bell shape.
• The values of the mean, median, and mode are equal.


All of the above are characteristics of a normal distribution.


Only some of the above are characteristics of a normal distribution.


None of the above are characteristics of a normal distribution.


Question 21
Let μ = 160 and σ = 16. Find the z-score for the score, x = 150.


-1.25


-0.625


0.675


0

Question 22
Let μ = 160 and σ = 16. Find the score x if the z-score = 1.


167


176


189


158


23

What proportion of the data from a normal distribution is within one standard deviation from the mean?


0.9544


0.6826


0.4772


0.5118


0.8733

24

The distribution of IQ scores for high school graduates is normally distributed with a mean of 105 and a standard deviation of 14. Identify the Excel statement that will find the probability that a person chosen at random from this group has an IQ score above 147.


=1-NORMSDIST(147)


=1-NORMSDIST(3)


=NORMSDIST(3)


=NORMSDIST(147)


=1-NORMSDIST(105)




25
EPA studies of fuel consumption indicate compact car mileage to be normally distributed with a mean of 25.4 and a standard deviation of 6 mpg. Identify the Excel statement that will find the percentage of compact cars that get between 23 and 40 mpg.


=[NORMSDIST(23)-NORMSDIST(40)]*100


=[1-NORMSDIST(23)-NORMSDIST(40)]*100


=[NORMSDIST(-0.4)+NORMSDIST(2.43)]*100


=[NORMSDIST(-0.4)-NORMSDIST(2.43)]*100


=[1-NORMSDIST(-0.4)-NORMSDIST(2.43)]*100
26
One year, the freshmen of all U.S. colleges had a mean average IQ of 107 and a standard deviation of 11. The IQ scores form a normal distribution. If a student is selected at random, find the probability that the student has an IQ below 100. Round your percentage to the hundredths


25.54%


26.23%


28.23%


30%







Question 27
Assume a normal distribution. A coin is tossed 100 times. Find the probability of 52 to 65 heads. Round your percentage to the hundredths place.


38.11%


32.45%


42.11%


36.45%


Question 28
Which statement is correct?
1. A point estimate is a single number that has been calculated to estimate the population parameter.
2. A point estimate is an estimate of the range of values for which an unknown, but true sample statistic lies.
3. A point estimate is a sample statistic such that the mean of all possible values equals the population parameter.
4. A point estimate is the sum of an estimator’s squared bias plus its variance.


Statement A


Statement B


Statement C


Statement D

Quesrion 29
Which statement is correct?
1. An interval estimate is a sampling procedure that matches each unit from Population A to a corresponding unit from Population
2. An interval estimate is an estimate of the range of values for which an unknown, but true sample statistic lies.
3. An interval estimate is a sample statistic such that the mean of all possible values equals the population parameter the statistic seeks to estimate.
D. An interval estimate is the sum of an estimator’s squared bias plus its variance


Statement A


Statement B


Statement C


Statement D



Question 30
A proportion of a college basketball team’s season ticket holders renew their tickets for the next season. Let ‘p’ denote the true proportion of ticket holders who buy tickets again for the following season. A random sample of 132 ticket holders revealed 93 people plan on renewing their tickets. Find the point estimate for ‘p’.


1.419354839


0.7045454545


0.2954545455


0.8345454545


0.4193548387





Question 31
Which statement is not correct?
A. The Central Limit Theorem of a sample proportion ‘p’ indicates that the mean of the sampling distribution of ‘p’ will be equal to the population proportion p.
B. The Central Limit Theorem of a sample proportion ‘p’ indicates that the sampling distribution of ‘p’ can be approximated by a normal distribution is np > 5 and nq > 5.
C. The Central Limit Theorem of a sample proportion ‘p’ is applied regardless of the sample size n and the population proportion p.
D. The Central Limit Theorem of a sample proportion ‘p’ is applied to non-normal populations.


Statement A


Statement B


Statement C


Statement D



Question 32
Which of the following sample sizes will produce a sampling distribution of the mean that is approximately normal?


10


20


30


All of the above.





Consider a large population with a mean of 150 and standard deviation of 27. A random sample of size 36 is taken from the population. Calculate the standard error of the sampling distribution of this sample mean and round your answer to the hundredths place.


5.10


4.80


4.60


4.20










Question 34
Compute the margin of error in estimating a population mean for a sample size of 6000 and a variance of 9. Round your answer to the thousandths place.


0.076


0.240


0.506


0.759






Question 35



If the standard deviation of a population is known and we wish to estimate the population mean with 98% confidence, what is the appropriate critical value ‘z’ to use?


2.58


2.33


1.96


1.645


1.28






Question 36
What does the interpretation of a 90% confidence interval estimate mean?


If we repeatedly draw samples of the same size from the same population, 90% of the values of the sample means will result in a confidence interval that includes the population mean


There is a 90% probability that the population mean will lie between the lower confidence limit (LCL) and the upper confidence limit (UCL).


We are 90% confident that we have selected a sample whose range of values does not contain the population mean.


There is a 10% probability that the population mean will lie between the lower confidence limit (LCL) and the upper confidence limit (UCL).


If we repeatedly draw samples of the same size from the same population, 10% of the values of the sample means will result in a confidence interval that includes the population mean.



Question 37

A random sample of 56 salespersons were asked how long on average they were able to talk to a potential customer. Their answers revealed a mean of 8.100000000 with a variance of 6 minutes. Construct a 95% confidence interval for the time it takes a salesperson to talk to a potential customer.


LCL = 8.058439402, UCL = 9.841560598


LCL = 7.458439402, UCL = 8.741560598


LCL = 6.958439402, UCL = 10.24156060


LCL = 7.958439402, UCL = 10.34156060


LCL = 6.858439402, UCL = 8.041560598


Question


38
A random sample of 74 people revealed it took an average (mean) of 60 minutes with a standard deviation of 10 minutes for a person to complete a loan application at the bank. Construct a 90% confidence interval for the true time it takes any person to complete a loan form.


LCL = 57.58772634, UCL = 63.41227366


LCL = 57.48772634, UCL = 61.21227366


LCL = 58.68772634, UCL = 63.01227366


LCL = 58.08772634, UCL = 61.91227366


LCL = 58.58772634, UCL = 63.51227366




Question 39 A statistical test of hypothesis consists of the five parts below. Place the parts in order, beginning with the first part.
1. State the conclusion.
2. Calculate the test statistic and its p-value.
3. Determine the alternate hypothesis.
4. Determine the null hypothesis.
5. Determine the rejection region.


A, B, C, D, E


D, C, A, B, E


C, D, B, E, A


D, C, B, E, A


D, C, E, B, A




Question 40
Complete the sentence: If we reject the null hypothesis, we conclude that _____ .


there is not enough statistical evidence to infer that the alternative hypothesis is true


there is not enough statistical evidence to infer that the null hypothesis is true


the test must be repeated


the test is statistically insignificant at the chosen level of significance

question 41
Which statement is an example of a null hypothesis?
A. A particular industrial process manufactures windshields with an average length of 33 inches.
B. The average quantity of detergent put into a box by a filling machine is not one pound.
C. The shipping company’s average delivery time is different from 3 days.
D. The average thickness of an aluminum sheet is not 0.03 inches, as required.


Statement A


Statement B


Statement C


Statement D


Question 42
A mail-order catalog claims that customers will receive their product within 4 days of ordering. A competitor believes this is an underestimate. State the appropriate null and alternative hypotheses to be tested by the competitor.


Ho: u > 4 vs. Ha: u

Ho: u > 4 vs. Ha: u = 4, where u = the average number of days until the product is received.


Ho: u = 4 vs. Ha: u

Ho: u

Ho: u = 4 vs. Ha: u > 4, where u = the average number of days until the product is received.



Question 43
A meteorologist claims that the average high temperature for the month of August in Philadelphia, PA. is 82 degrees Fahrenheit. If the residents of Philadelphia do not believe this to be true, what hypotheses should they test?


Ho: u > 82 degrees Fahrenheit vs. Ha: u

Ho: u = 82 degrees Fahrenheit vs. Ha: u

Ho: u 82 degrees Fahrenheit


Ho: u = 82 degrees Fahrenheit vs. Ha: u does not = 82 degrees Fahrenheit


Ho: u = 82 degrees Fahrenheit vs. Ha: u > 82 degrees Fahrenheit


Question 44
The manufacturer of a particular battery pack for laptop computers claims its battery packs can function for 9 hours, on the average, before having to be recharged. A competitor claims that the manufacturer’s claim is too high. A random sample of 38 battery packs was selected and placed on test. The mean functioning time before having to be recharged was 7.2 hours with a standard deviation of 1.5 hours. Perform the appropriate test of hypothesis to determine whether the competitor is correct. Test using alpha = 0.05. Calculate the test statistic and round your answer to the hundredths place.


Test statistic = -9.06


Test statistic = -4.56


Test statistic = -6.79


Test statistic = -7.40


Test statistic = -3.26






Question 45
The manufacturer of a particular battery pack for laptop computers claims its battery packs can function for 9 hours, on the average, before having to be recharged. A competitor claims that the manufacturer’s claim is too high. A random sample of 37 battery packs was selected and placed on test. The mean functioning time before having to be recharged was 7.4 hours with a standard deviation of 1.7 hours. Perform the appropriate test of hypothesis to determine whether the competitor is correct. Test using alpha = 0.05. Based on the test statistic, what can you conclude?


Test statistic = -7.464425433, so we should reject the manufacturer’s claim.


Test statistic = -34.82352941, so we should reject the manufacturer’s claim.


Test statistic = -5.724952969, so we should reject the manufacturer’s claim.


Test statistic = -34.82352941, so we should not reject the manufacturer’s claim.


Test statistic = -5.724952969, so we should not reject the manufacturer’s claim.







Question 46
A sample size of 150 is to be used to test the hypotheses
H0: µ = 8.3 vs. Ha: µ ≠ 8.3
where µ is the true average weight of a newborn American baby. Determine the appropriate rejection region with a significance level of alpha = 0.05.


Reject H0 if z >2.58 or z

Reject H0 if z -2.58


Reject H0 if z >1.96 or z

Reject H0 if z -1.96


Reject H0 if z >1.645 or z

Reject H0 if z -1.645








Question 47
A sample size of 80 is to be used to test the hypotheses
H0: µ = 29 vs. Ha: µ > 29
where µ is the true average age of a person when he/she gets married. Determine the appropriate rejection region with a significance level of alpha/2 = 0.005.


Reject H0 if z >2.33


Reject H0 if z >2.58


Reject H0 if z >1.645


Reject H0 if z >1.28




Question 48
In a hypothesis test, the test statistic was calculated to be 1.76. The rejection region is -2.33

The null hypothesis is accepted to be true.


The null hypothesis is rejected since the test statistic is within the rejection region.


The null hypothesis is not rejected since the test statistic is within the rejection region.


The null hypothesis is rejected since the test statistic proves it to be false.


Question 49
When the alternative hypothesis is formulated in a large-sample statistical test as µ > µ0 or µ

One-tailed test


Two-tailed test


Type I test


Type II test

What are the two types of errors that can be made in hypothesis testing?


Exception and Rejection


Type I and Type II


Analytical and Iterative


Propogation and Human Error


yes
no

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