Question

Assignment 7 Please answer all the questions using the appropriate version of the dataset as assigned by your TA. Each graph must be labeled with a title, axis labels, and a footnote with your name and section number 1. For this example, you will enter the data directly into the Data Window. Start by closing the current worksheet. Here is a random sample of resting heart rates for 20 male athletes between the ages of 18 and 25: 58 67 63 65 59 57 51 64 59 54 65 56 59 58 62 64 55 59 61 55 You are interested in constructing a confidence interval for Ji, the average heart rate of all male athletes in this age group Since this is a small data set it is critical that the assumption of Normality is satisfied. So, begin with a graph that will look for normality (or lack of normality). Copy and paste the graph into your Word document. Construct a 99% confidence interval for 1, the average heart rate of all male athletes in this age group. Include the Confidence Interval from your Session Window and the Histogram and Boxplot of the data b. What do the graphs (probability plot, Histogram and Boxplot) tell you about the dataset? c Using the confidence interval, make a statement about, the average resting heart rate of male athletes. 2. Suppose you are interested in estimating the average salary for Biostatisticians in Connecticut. You obtain a random sample of 25 biostatisticians hired during the last five years. The sample data appeared to be approximately normally distributed with no outliers. The average salary for the sample is $80,080 and the standard deviation is $18,850. Construct a 95% confidence interval for u the true average salary for newly hired biostatisticians in Connecticut. Note: In this example, you have the summarized data, rather than the raw data. Click on: STAT - BASIC STATISTICS 1-SAMPLE- On the input screen, use the drop-down menu to select Summarized Data and enter the sample size, the sample mean and the sample standard deviation. Using the confidence interval, make a statement about Ji, the average starting salary of Biostatisticians in CT. Include the Confidence interval from your Session Window.

Answer 1

To construct a confidence interval for a population mean, a t-distribution is used for small samples after checking normality, while a normal distribution is used for large samples or if the population is assumed to be normal. The interval includes the sample mean and a margin of error based on the standard deviation and a z-score or t-score.

Step-by-step explanation:

To construct a confidence interval for the population mean using the data provided, one must first determine the appropriate distribution to use. For small samples (n < 30) that do not follow a normal distribution, the t-distribution should be used after checking for normality with plots such as the histogram and boxplot. However, if the sample size is large enough, or if we can assume that the sampled population is normally distributed, the normal distribution is appropriate.

For a population mean, the confidence interval generally takes the form of the sample mean ± the margin of error. The margin of error is calculated using either the z-score or t-score multiplied by the standard deviation divided by the square root of the sample size. For a 95% confidence interval using a normally distributed large sample, you would use the z-score; for small samples, the t-score from the t-distribution would be used.

For example, to construct a 95% confidence interval for biostatistician salaries in Connecticut with a sample mean of $80,080 and sample standard deviation of $18,850 for 25 entries, you would use the t-distribution since the sample size is below 30. The same approach would apply to the context of resting heart rates for athletes and television viewing habits of statistics students.