Head Circumference Analysis: Descriptive Statistics and Confidence Intervals, Papers of Statistics

Download Head Circumference Analysis: Descriptive Statistics and Confidence Intervals and more Papers Statistics in PDF only on Docsity! HEAD CIRCUMFERENCE Use the following data sets that have been downloaded into your calculator FHED = Head circumferences of Two-Month-Old Baby-Girls (cm) MHED = Head circumferences of Two-Month-Old Baby-Boys (cm) Chapter 1 1) Answer each of the following: a) Identify the population(s), and variable b) Is the variable qualitative or quantitative? c) Is the variable discrete or continuous? d) Identify the level of measurement. e) What sampling technique could have been used? f) Is this an observational study or an experiment? 1 HEAD CIRCUMFERENCE Chapter 2 – Constructing a frequency distribution 2) a) Construct a frequency distribution for the head circumferences of baby boys and construct a separate frequency distribution for the head circumferences of baby girls. In both cases, use the classes of 34.0-35.9, 36.0-37.9, and so on. b) Compare the results and determine whether there appears to be a significant difference between the two genders. c) The largest relative frequency for the baby boys’ distribution is ____________. It corresponds to the class____________ d) _________% of the girls in the sample had a head circumference between 38.0 and 39.9 cm inclusive. e) For the males’ distribution, the cumulative frequency corresponding to the class 40.0-41.9 is ____________ f) Use the same set of axes to construct the two corresponding frequency polygons. g) True or False? The median of the females’ distribution is in the class 38.0-39.9 2 HEAD CIRCUMFERENCE Chapter 7 – Distribution of Sample Mean 5) Past results from the National Health Survey suggest that the head circumferences of 2- month-old boys are normally distributed and have a mean of 41.1 cm and a standard deviation of 1.5 cm. a) Give the shape, mean and standard deviation of the distribution of sample means for samples of size 50. b) What is the probability that a sample of fifty 2-month-old babies have a head circumference of at most 40.048 cm? c) If the population has a mean of 41.1 cm, the probability that a sample of size fifty has a mean of 40.048 or less is ___________________ This means that for samples of size 50, about _________ samples in 10 million will result in a sample mean of 40.048 or less when the population mean is 41.1 Because this event only happens______ out of ______________ times, we consider it to be usual/unusual. d) What may this result suggest? 5 HEAD CIRCUMFERENCE Chapter 8 – Confidence Intervals about a Population Mean mu 6) a) Estimate the mean head circumference of all baby-girls that are two months old by constructing a 99% confidence interval.  We start by selecting a simple random sample of size n. In our calculator we actually have one such a sample labeled FHED  We calculate the mean of the selected sample. This is our point estimate. x =  To fine-tune our estimate, we find a confidence interval which is a range (or interval) of values that is likely to contain the true value of the population mean. Show all work, and then check with a calculator feature (Are you using z or t? Why?) b) Complete the following: (i) With 99% confidence we can say that the mean head circumference of two-month-old baby girls is ______ with a margin of error of _______ (ii) We are ____% confident that the interval from __________ to _________ actually does contain the true value of the population mean μ. This means that if we were to select many different samples of the same size and construct the corresponding confidence intervals, in the long run ______% of them would actually contain the value of μ. (iii) For 99% of such intervals, the sample mean would not differ from the actual population mean by more than _______ 6 HEAD CIRCUMFERENCE Chapter 8 – Confidence Intervals about a Population Mean mu 7) a) Estimate the mean head circumference of all baby-boys that are two months old by constructing a 99% confidence interval.  We start by selecting a simple random sample of size n. In our calculator we actually have one such a sample labeled MHED  We calculate the mean of the selected sample. This is our point estimate. x =  To fine-tune our estimate, we find a confidence interval which is a range (or interval) of values that is likely to contain the true value of the population mean. Show all work, and then check with a calculator feature. (Are you using z or t? Why?) b) Complete the following: (i) With 99% confidence we can say that the mean head circumference of two-month-old baby boys is ______ with a margin of error of _______ (ii) We are ____% confident that the interval from __________ to _________ actually does contain the true value of the population mean μ. This means that if we were to select many different samples of the same size and construct the corresponding confidence intervals, in the long run ______% of them would actually contain the value of μ. (iii) For 99% of such intervals, the sample mean would not differ from the actual population mean by more than _______ c) Compare with the results of the previous page. Does there appear to be a significant difference between the two genders? Explain. 7