1. � Follow the steps to compute the variance and standard deviation for the following population. 49 51 53 55 57 59 61 2. � For a sample of 289 female heights, the mean was 65.3 inches and the standard deviation was 2.8 inches. The shortest person in this sample had of 56 inches. a. � Find the z-score for the height of 56 inches. b. � What does the negative sign for the z-score represent? c. � Is this observation a potential outlier according to the three standard deviation distance criterion? Explain. 3. � A company decides to investigate the amount of sick leave taken by its employees. A sample of seven employees yields the following numbers of days of sick leave taken in the past year. 1 1 3 0 1 6 2 Use this information to answer parts a through c. 4. � What is the effect of the outlier? 5. � A survey asked 6189 random adults the question “How many children have you ever had?”� Use the results shown below to answer the following questions. # no of children � � 0 � � � � 1 � � � 2 � � 3 � � 4 � � 5 � � 6 � � 7 n � 1851 � � 869 � � 1462 � 945 � 494 � 281 � 153 � 93 a. � Find the standard error of the sample mean of the random sample of 6189 adults. b. � Construct a 95% confidence interval for the population mean µ. Can it be concluded that the population mean is less than 2.0? c. � On what assumptions is the analysis in part (b) based? Is the assumption of randomization valid? Is the assumption that the population distribution is approximately normal a valid assumption? 6. � A survey asked the question “What do you think is the ideal number of children for a family to have?”� The 473 females who responded had a median of 2, mean of 3.13, and standard deviation of 1.48. Answer parts a-d. a. � What is the point estimate of the population mean? b. � Find the standard error of the sample mean. c. � The 95% confidence interval is (3,3.26). Interpret. d. � Is it plausible that the population mean µ = 2?
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