Essays on Statistics Problem Solving Math Problem

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QUESTION 1A study is under way in Yosemite National Forest to determine the adult height of American pine trees. Specifically, the study is attempting to determine what factors aid a tree in reaching heights greater than 60 feet tall. It is estimated that the forest contains 25,000 adult American pines. The study involves collecting heights from 250 randomly selected adult American pine trees and analyzing the results. Identify the population from which the study was sampled. the 250 randomly selected adult American pine treesVthe 25,000 adult American pine trees in the forestall the adult American pine trees taller than 60 feetall American pine trees, of any age, in the forestQUESTION 2TABLE 2-5 The following are the durations in minutes of a sample of long-distance phone calls made within the continental United States reported by one long-distance carrier. Time (in minutes)RelativeFrequency0 but less than 50.375 but less than 100.2210 but less than 150.1515 but less than 200.1020 but less than 250.0725 but less than 300.0730 or more0.02Referring to Table 2-5, what is the cumulative relative frequency for the percentage of calls that lasted 10 minutes or more? 0.160.24V0.410.90QUESTION 3In a perfectly symmetrical distributionthe range equals the interquartile range. the interquartile range equals the arithmetic mean. Vthe median equals the arithmetic mean. the variance equals the standard deviation. QUESTION 4True or False: In a set of numerical data, the value for Q2 is always halfway between Q1 and Q3.TrueVFalseQUESTION 5If we know that the length of time it takes a college student to find a parking spot in the library parking lot follows a normal distribution with a mean of 3.5 minutes and a standard deviation of 1 minute, find the point in the distribution in which 75.8% of the college students exceed when trying to find a parking spot in the library parking lot. V2.8 minutes (mean – 0.7 st.

dev. )3.2 minutes3.4 minutes4.2 minutesQUESTION 6True or False: A worker earns $15 per hour at a plant and is told that only 2.5% of all workers make a higher wage. If the wage is assumed to be normally distributed and the standard deviation of wage rates is $5 per hour, the average wage for the plant is $7.50 per hour. TrueVFalse – 2 st.

dev. below $15 = $5QUESTION 7For sample sizes greater than 30, the sampling distribution of the mean will be approximately normally distributedregardless of the shape of the population. only if the shape of the population is symmetrical. only if the standard deviation of the samples are known. Vonly if the population is normally distributed. QUESTION 8True or False: Suppose μ = 50 and σ2 = 100 for a population. In a sample where n = 100 is randomly taken, 95% of all possible sample means will fall between 48.04 and 51.96.VTrueFalseQUESTION 9Suppose a 95% confidence interval for μ has been constructed. If it is decided to take a larger sample and to decrease the confidence level of the interval, then the resulting interval width would __________.

(Assume that the sample statistics gathered would not change very much for the new sample. )be larger than the current interval widthVbe narrower than the current interval widthbe the same as the current interval widthbe unknown until actual sample sizes and reliability levels were determinedQUESTION 10True or False: The t distribution approaches the standardized normal distribution when the number of degrees of freedom increases. VTrueFalseQUESTION 11The owner of a local nightclub has recently surveyed a random sample of n = 250 customers of the club.

She would now like to determine whether or not the mean age of her customers is over 30. If so, she plans to alter the entertainment to appeal to an older crowd. If not, no entertainment changes will be made. Suppose she found that the sample mean was 30.45 years and the sample standard deviation was 5 years. If she wants to be 99% confident in her decision, what conclusion can she make? VThere is not sufficient evidence that the mean age of her customers is over 30.There is sufficient evidence that the mean age of her customers is over 30.There is not sufficient evidence that the mean age of her customers is not over 30.There is sufficient evidence that the mean age of her customers is not over 30.QUESTION 12True of False: The larger is the p-value, the more likely one is to reject the null hypothesis. TrueVFalseQUESTION 13The residuals representthe difference between the actual Y values and the mean of Y. Vthe difference between the actual Y values and the predicted Y values. the square root of the slope. the predicted value of Y for the average X value. QUESTION 14

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