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Statistical Analysis and Hypothesis Testing: A Comprehensive Assignment

An assignment on hypothesis testing and its practical applications in statistical analysis.

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    Statistical Analysis and Hypothesis Testing: A Comprehensive Assignment 1. True or False. Justify for full credit. (a) The volume of milk in a jug of milk is 128 oz. The value 128 is from a discrete data set. False - The value 128 is a measure of volume which is a continuous variable and can have values other than counting numbers. A volume of 128.2 for example is possible. (25 pts) . (b) If the variance from a data set is zero, then all the observations in this data set must be zero. False - If t he variance from a data set is zero, then all the observations in this data set must be equal. . (c) P ( A AND A c ) = 0, where A c is the complement of A . True ( A AND A c ) is the intersection of A and its complement and by definition it is null. . (d) The mean and median for a normal distribution are always the same. True - The normal distribution is a bell - shaped distribution and symmetrical about the mean, therefore the mean=median. . (e) In a hypothesis testing, if the p - value is less than the significance level α, we do not have sufficient evidence to reject the null hypothesis. False If the p - value is less than the significance level α, have sufficient evidence to reject the null hypothesis, since the test statistic lies in the rejection region. Refer to the following frequency distribution for Questions 2, 3, 4, and 5. Show all work. Just the answer, without supporting work, will receive no credit. A random sample of 25 customers was chosen in UMUC MiniMart between 3:00 and 4:00 PM on a Friday afternoon. The frequency distribution below shows the distribution for checkout time (in minutes). Checkout Time (in minutes) Frequency Relative Frequency 1.0 - 1.9 6 =6/25 *100= 24

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    2.0 - 2.9 8 =8/25 *100= 32 3.0 - 3.9 6 24 4.0 - 5.9 5 =5/25 *100= 20 Total 25 100 2. Complete the frequency table with frequency and relative frequency. 3. What percentage of the checkout times was less than 3 minutes? =24+32= 56% 4. In what class interval must the median lie? Explain your answer. 2.0 - 2.9 , since the cumulative frequency corresponding to this interval is 56% and the median which is the 50 th percentile is included in this interval. 5. Assume that the largest observation in this dataset is 5.8. Suppose this observation were incorrectly recorded as 8.5 instead of 5.8. Will the mean increase, decrease, or remain the same? Will the median increase, decrease or remain the same? Why? (5 pts) The mean will increase , as the sum of the observations is increased by 2.7 and the number of observations is the same. The median remains the same, since only the highest observation was affected. Refer to the following information for Questions 6, 7, and 8. Show all work. Just the answer, without supporting work, will receive no credit. A 6 - faced die is rolled two times. Let A be the event that the outcome of the first roll is an even number, and B be the event that the outcome of second roll is greater than 4. 6. How many outcomes are there in the sample space? (5 pts) A : 3*6= 18 outcomes B: 6*2= 12 outcomes 7. What is the probability that the outcome of the second roll is greater than 4, given that the first roll is an even number? (10 pts) P(B|A)= P(AB)/P(A) P(A)= 18/6*6 = 18/36 =1/2 P(AB)=3*2/6*6 =1/6 P(B|A)= P(AB)/P(A)=( 1/6)/1/2= 2/6= 1/3 8. Are A and B independent? Why or why not? Yes as P(AB)= P(A)*P(B) — 1/6= ½*1/3= 1/6

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