1.(1) The claim by a weight loss Company is that on average, the client will lose 10 pounds over
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first 2 weeks. 50 people who joined the programme are sampled, their weight loss is 9 pounds with a standard deviation of 2.8 pounds. Can we conclude at the .05 level that a person joining the programme will lose less than 10 pounds?
(2) The following is a random sample of 90-day futures prices in dollars for 1 troy oz. of silver from The Wall Street Journal issues in May and June of 1997: 4.74, 4.77, 4.87, 4.91, 4.83, 4.72, 4.92, 4.86, 4.97, 4.71, 4.90, 4.93, 4.75, 4.88, 4.79, 4.83, 4.89.
Required:
a. Calculate the mean
b. Median
c. Standard deviation of the 90-day future price of silver data
(3) A mining company needs to estimate the average amount of copper ore per ton mined. A random sample of 50 tons gives a sample mean of 146,75 pounds. The population standard deviation is assumed to be 35.2 pounds.
Required:
a. Give a 95% confidence interval for the average amount of copper in the population of tons mined.
b. Give a 90% confidence interval for the average amount of coper per ton
c. Give a 99% confidence interval for the average amount of coper per ton
(4) An e-commerce Website gets 2,385 visitors on a particular day. Among these, 1790 visitors explore the products by looking at more pages at the site. Among these 1790 visitors who explore the products, 387 make a purchase.
Required:
a. If a visitor chosen at random from all those who visited the site, what is the probability that the visitor explored the products
b. If a visitor is chosen at random from all those who visited the site, what is the probability that the visitor made a purchase.
c. If a visitor is chosen at random from all those who explored the products, what is the probability that the visitor made a purchase.
d. Which of the preceding three probabilities is relevant to the design of the home page that leads to product page.
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21.Suppose the heights of 18-year-old men are approximately normally distributed, with mean 65 inches and standard deviation 6 inches.
A button
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nd standard deviation 6 inches.
A button hyperlink to the SALT program that reads: Use SALT.
(a) What is the probability that an 18-year-old man selected at random is between 64 and 66 inches tall? (Round your answer to four decimal places.)
Correct: Your answer is correct.
(b) If a random sample of seven 18-year-old men is selected, what is the probability that the mean height x is between 64 and 66 inches? (Round your answer to four decimal places.)
Incorrect: Your answer is incorrect.
(c) Compare your answers to parts (a) and (b). Is the probability in part (b) much higher? Why would you expect this?
The probability in part (b) is much higher because the standard deviation is smaller for the x distribution.
The probability in part (b) is much higher because the standard deviation is larger for the x distribution.
The probability in part (b) is much higher because the mean is smaller for the x distribution.
The probability in part (b) is much higher because the mean is larger for the x distribution.
The probability in part (b) is much lower because the standard deviation is smaller for the x distribution.
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22.A food company wishes to determine whether a newly designed potato chip bag increases the length of time a bag
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time a bag of chips remains fresh on the grocery shelf. A random sample of potato chips with the old design of the bag was compared to a random sample of potato chips with the new bag. Summary statistics pertaining to the number of days the chips remained fresh are given below. At a 95% level of confidence (α = .05), the company wishes to investigate if the new bag has an increased freshness time over the old bag.
Summary Statistics
New Bag Old Bag
(Sample #1) (Sample #2)
Sample Mean 21.2 days 20.8 days
Sample Standard Deviation 2.5 days 2.8 days
Sample Size 45 50
What is the correct Null and Alternate Hypothesis?
Select one:
a. H_0: \mu_d>0\;\; H_1: \mu_d < 0
b. H_0: \mu_1>\mu_2 \;\;H_1:\mu_1 \leq \mu_2
c. H_0: \mu_d =0\;\; H_1: \mu_d < 0
d. H_0: \mu_1\leq\mu_2 \;\;H_1:\mu_1 > \mu_2
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27.
Risk taking is an important part of investing. In order to make suitable investment decisions on behalf of their customers,
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ehalf of their customers, portfolio managers give a questionnaire to new customers to measure their desire to take financial risks. The scores on the questionnaire are approximately normally distributed with a mean of 49 and a standard deviation of 14 The customers with scores in the bottom 10% are described as "risk averse." What is the questionnaire score that separates customers who are considered risk averse from those who are not? Carry your intermediate computations to at least four decimal places. Round your answer to one decimal place.
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28.Fox News recently reported the results of a public opinion poll on supporting Trump that asked:
“Since he became the president,
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Since he became the president, did President Trump act with the transparency and the integrity
that you expect from a president?” 675 voters responded the poll and 351 responded “YES.”
Assume that 40% of the U.S. population supports Trump.
a. Define a binary random variable, Y, for supporting Trump (Y=1) vs. not (Y=0).
Calculate the population mean (????????) and variance (????????
2
) for supporting Trump.
b. Calculate the sample mean ????̅ and the sample standard deviation of ????̅ (????????̅ ) for the poll.
c. Calculate the standard error of ????̅ and construct a 95% confidence interval from the
poll using ????̅ and its sample standard error.
d. Conduct a two-sided hypothesis test at 5% significance level to determine whether
40% of the U.S. population supports Trump. State the null and the alternative
hypotheses, calculate the test statistics and the associated p-value, and conclude. Is
the Fox News survey reliable? Why? Why Not?
e. Suppose that you wanted to design a survey that had a margin of error of at most 1%.
That is: the difference between the upper bound and the lower bound of the
confidence interval should be a maximum of 2 percentage points. For example, for
????̅ = 0.52 you are aiming for the 95 % CI to be [0.51 0.53].
How large should n be if the survey uses simple random sampling?
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44.2.
PODStat5 4.E.031.
The standard deviation alone does not measure relative variation. For example, a standard deviation of $1 would be considered
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, a standard deviation of $1 would be considered large if it is describing the variability from store to store in the price of an ice cube tray. On the other hand, a standard deviation of $1 would be considered small if it is describing store-to-store variability in the price of a particular brand of freezer. A quantity designed to give a relative measure of variability is the coefficient of variation. Denoted by CV, the coefficient of variation expresses the standard deviation as a percentage of the mean. It is defined by the formula CV = 100(s/ x ). Consider two samples. Sample 1 gives the actual weight (in ounces) of the contents of cans of pet food labeled as having a net weight of 8 oz. Sample 2 gives the actual weight (in pounds) of the contents of bags of dry pet food labeled as having a net weight of 50 lb. There are weights for the two samples.
Sample 1 7.7 6.8 6.5 7.2 6.5
7.7 7.3 6.6 6.6 6.1
Sample 2 50.7 50.9 50.5 50.3 51.5
47 50.4 50.3 48.7 48.2
(a) For each of the given samples, calculate the mean and the standard deviation. (Round all intermediate calculations and answers to five decimal places.)
For sample 1
Mean
Standard deviation
For sample 2
Mean
Standard deviation
(b) Compute the coefficient of variation for each sample. (Round all answers to two decimal places.)
CV1
CV2
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50.Statistics help. Find the mean and standard deviation for the 65 low prices in your sample and provide the printout
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de the printout below. Use these values as estimates of the mean and standard deviation found in the population of all low prices. Suppose that the low prices were normally distributed (regardless of what your data may indicate). Find the proportion of all low prices that would be between $20 and $50 in the population. I want you to show your work. To receive full credit, you should include pictures of the normal curve (labeled with both x and z-values) with the pertinent probabilities shaded in the picture
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52.
The Indigo Insurance Company is a large company based in Melbourne. Several years ago, an email survey of all their
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survey of all their employees found that employees were required to respond to an average of 50 work-related emails per week with a standard deviation of 1.5 emails per week. However, an employee advocacy group believes the average number of work-related emails Indigo Insurance Company employees are now required to respond to is more than 50 emails per week.
To investigate this further, the employee advocacy group took a random sample of 20 staff employed by Indigo Insurance Company during the second week of March 2018,and asked these employees to record the number of work-related emails to which they were required to respond.
(b). What does the highlighted section of the distribution in Figure 1 represent?
(c). The random sample of 20 employees of Indigo Insurance Company taken by the employee advocacy group turned out to have a mean of 50.8 work-related emails to respond to in that week. Does this sample look like it belongs to the sampling distribution displayed in Figure 1? Justify your answer.
(d). Given the sample was randomly selected and that the number of work-related emails each employee was required to respond to was recorded accurately, what conclusion can we reach from part (c)?
To answer questions (b) to (d), consider the sampling distribution shown in Figure 1.
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55.These are the questions I need to answer
A researcher examines whether the clinically anxious individuals differ from people in
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viduals differ from people in general in remembering threatening information. The memory performance of an individual for negative words was measured and was found to have a score of 48. The population average is 34 with a standard deviation of 9. At the 5% level of significance what should you conclude about whether clinically anxious individuals have a tendency to remember threatening words?
(a) Clearly state null and research hypotheses in terms of the mean scores on the memory performance on negative words, μ, of anxious individuals.
(b) What is the comparison distribution for the sample’s Z score?
(c) What are the cut-off values for a test with significance level 0.05?
(d) What is the observed Z score?
(e) What is your conclusion?
An educational psychologist was interested in whether children who grow up in bilingual settings have an advantage of distraction resistance compared with children in general. The distraction resistance test was administered to a randomly chosen child with bilingual upbringing background who was found to have a score of 69. The population average is 60 with a standard deviation of 3. Do children with bilingual upbringing background score higher on distraction resistance test than children in general? Use the 1% level of significance.
(a) Clearly state null and research hypotheses in terms of the mean scores on distraction resistance, μ, of children with bilingual upbringing.
(b) What is the comparison distribution for the sample’s Z score?
(c) What are the cut-off values for a test with significance level 0.01?
(d) What is the observed Z score?
(e) What is your conclusion?
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57.1. The amount of chilli sauce dispensed from a machine at a local food joint is normally distributed with a
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with a mean of 25 gm and a standard deviation of 5 gm.
(a) If the machine is used 500 times, approximately how many times will it be expected to dispense 30 gm or more of chilli sauce?
(b) How can you decrease this number to half? Give a numerical answer.
2. StarTech manufactures re sensors. They use a protective screen for their sensors to protect it from dust. The sensor becomes useless if the thickness of the screen exceeds 0.5 mm. They outsource the production of the screen to a di erent company that claims to manufacture screens with a mean thickness of 0.3 mm and a standard deviation of 0.1 mm.
(a) If 10000 screens are manufactured how many will be discarded because they are too thick?
(b) If screens less than 0.2 mm are too thin to be used, what is the probability that screens manufactured by the above company will be discarded because they are too thick or too thin? Show the result on a graph.
3. The amount of time that Sam spends playing the guitar is normally distributed with a mean of 15 hours and a standard deviation of 3 hours.
(a) Find the probability that he spends between 15 and 18 hours playing the guitar during a given week.
(b) What is the probability that he spends less than 3 hours playing the guitar during a given week?
4. Soon after he took oce in 1963, President Johnson was approved by 160 out of a sample of 200 Americans. With growing disillusionment over his Vietnam policy, by 1968 he was approved by only 70 out of a sample of 200 Americans.
(a) What is the 90% con dence interval for the percentage of all Americans who approved of Johnson in 1963? In 1968?
(b) What is the 90% con dence interval for the change?
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