Create a research problem that would use a statistic that would explore differences(not relationships) related to something of interfere to you then identify the following: (a) population (b) sample (c) research hypothesis, (d) null hypothesis (e) the variables (f) the inferential statistics that you might use and why.
In: Math
Suppose that you are interested in estimating the average number of miles per gallon of gasoline your car can get. You calculate the miles per gallon for each of the next twenty-five times you fill the tank. Suppose that in truth, the values for your car are bell-shaped, with a mean of 20 miles per gallon and a standard deviation of 1. Find the possible sample means you are likely to get based on your sample of twenty-five observations. Consider the intervals into which 68%, 95%, and almost all of the potential sample means will fall, using the Empirical Rule. (Round all answers to the nearest thousandth.)
About 68% of possible sample means will be in the range between ___ and ____ .
About 95% of possible sample means will be in the range between ____ and ____ .
About 99.7% of possible sample means will be in the range between ____ and ____.
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The weight of football players in the NFL is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds.
A) What is the probability that a randomly selected football player will weigh more than 243.75 pounds?
B) What is the probability that a football player will weigh less than 260 pounds?
C) What percentage of players will weigh between 150 to 250 pounds?
D) 95% of player weights are less than X pounds. Therefore X is?
In: Math
A random sample of 81 observations is drawn from a population with a mean of 104 and a variance of 156.25.
a) State the distribution of the sample mean, ?̅. (Show any conditions that you have checked.)
b) Calculate the probability that the sample mean is at most 102.5.
c) Calculate the probability that the sample mean is between 103.5 and 105.8.
In: Math
7.A random sample of 49 observations is drawn from a population with a normal distribution. If the sample mean is 265 and the sample standard deviation is 57, find the 95% confidence interval for the population mean.
8. A random sample of 49 observations is drawn from a population with a normal distribution with a standard deviation of 57. If the sample mean is 265, find the 95% confidence interval for the population mean. Compare this confidence interval with the one found in question 7. Finally, find the 99% confidence interval for the population mean. How does this compare to the 95% confidence interval?
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The wait time at the Goleta Post Office is uniformly distributed between 1 and 16 minutes.
a) Define the random variable of interest, X.
b) State the distribution of X.
c) What is the average wait time?
d) Calculate the probability that the wait time is more than 17 minutes.
e) Calculate the probability that the wait time is at least 10 minutes.
f) Calculate the probability that the wait time is between 2 and 11 minutes
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A researcher is interested in the mean amount of time it takes people to complete a personality questionnaire. He selects 40 people at random and calculates the mean amount of time to be 20.4 min with a variance of 17.64 min2 .
a) Define the parameter of interest.
b) Define the random variable of interest.
c) Name the distribution required to calculate confidence intervals. (Check the relevant criteria.)
d) Construct a 98% confidence interval for the true mean amount of time.
e) Interpret your confidence interval.
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A university has 15,000 students. We have drawn a simple random sample size of 400 from the population and recorded how much money each student spent on cellular telephone service during November 2003. For this sample, the sample mean is $36, and sample standard deviation is $20. At a 99% level of confidence, test the null hypothesis that these 15,000 students, combined, did not spend more than $500,000 on cellular telephone service during November 2003.
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A computer manufacturer believes that the proportion of hardware malfunctions is different in humid climates than in dry climates. To test this claim, the manufacturer takes a random sample of 400 machines sold in Florida (humid) and 400 machines sold in Arizona (dry). The manufacturer finds that 44 of the machines in Florida and 24 of the machines in Arizona had hardware malfunctions.
a. Specify the competing hypotheses to test the manufacturer's claim.
b. Calculate the value of the relevant test statistic.
c. Compute the p-value. Does the evidence support the computer manufacturer's claim at the 10% significance level?
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Name and discuss four probability distributions , highlight their characteristics , how they are similar to one another , and how they differ from one another , and hoe they differ from one another?
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A worker for measurement Canada suspects a gas station chain has calibrated its pumps to deliver less fuel than advertised. 15 pumps are sampled by dispensing gas into a graduated container, until the metered amount of gasis exactly 40 L. From your sample, you calculate the mean amount dispensed is x̅ = 39.7 L, with s = 0.6 L. At the α = 0.05 level of signifciance, test the hypothesis that the station pumps deliver less than 40 L. Assume that all conditions for testing hypothesis have been met.
a) Clearly defining any symbols, state the null and alternative hypothesis in symbolic form?
b) Calculate the value of the test statistic for testing above hypothesis
c) Calculate only one of the rejection region or the p-value for the above test.
d) State the conclusion and interpretation for the test
e) Describe the consequences of a type I error in this scenario.
In: Math
Suppose that the lifetimes of light bulbs are approximately normally distributed, with a mean of
56 hours and a standard deviation of 3.3 hours. With this information, answer the following questions.
(a) What proportion of light bulbs will last more than61 hours?
(b) What proportion of light bulbs will last51 hours or less?
(c) What proportion of light bulbs will last between59 and 62 hours?
(d) What is the probability that a randomly selected light bulb lasts less than 45 hours?
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The following data represent a company's yearly sales volume and its advertising expenditure over a period of 5 years. (Y) Sales in Millions of Dollars 15 16 18 17 16 (X) Advertising in ($10,000) 32 33 35 34 36
(a) Compute the coefficient of determination for the estimated regression equation you got in the previous in-class problem.
(b) Interpret the meaning of the value of the coefficient of determination that you found in (a). Be very specific.
(c) Perform a t test and determine whether or not X and Y are related. Let = 0.05.
(d) Perform an F test and determine whether or not X and Y are related. Let = 0.05.
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Paint-Drying Robots. How long it takes paint to dry can have an
impact on the production capacity of a business. In May 2018,
Deal’s Auto Body & Paint in Prescott, Arizona, invested in a
paintdrying robot to speed up its process (The Daily Courier
website, https://www.dcourier.com/photos/2018/may/26/984960336/).
An interesting question is, “Do all paintdrying robots have the
same drying time?” To test this, sup pose we sample five drying
times for each of different brands of paintdrying robots. The time
in minutes until the paint was dry enough for a second coat to be
applied was recorded. The following data were obtained.
Robot 1: 128 137 135 124 141
Robot 2: 144 133 142 146 130
Robot 3 : 133 143 137 136 131
Robot 4: 150 142 135 140 153
At the a = .05 level of significance, test to see whether the mean
drying time is the same for each brand of robot
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Teleconferences, electronic mail, and word processors are among
the tools that can
reduce the length of business meetings. A recent survey indicated
that the percentage
reduction y in time spent by business professionals in meetings due
to an automated office
equipment is approximately normally distributed with mean equal to
15% and standard
deviation equal to 4%.
a. what proportion of all business professionals with access to
automated office equipment
have reduced their time in meetings by more than 22%
a. what proportion of all business professionals with access to
automated office equipment
have reduced their time in meetings by 10 % or less?
In: Math