Homework 07: t-Distribution

1. Say that a 90% confidence interval for a population mean is given as (9.89, 11.03), and
that this confidence interval is based on a simple random sample of 81 observations.
Calculate the sample mean and sample standard deviation. Use the t-distribution
in any calculations.
2. Let’s look at analyzing a real data set and acquiring all the information we need to
perform a hypothesis test. Please describe the data, your analysis, and your findings
using complete sentences. Use the data set named finches found at the underlined link.
All units are in millimeters. You may want to reference the Lecture 7 examples file for
an easier time loading in the data set.
(a) Make and describe an appropriate plot for the ”taillength” variable. In your
description, include any observations you make regarding the skew (if there is
any) and possible outliers.
(b) Calculate and interpret a 95% confidence interval for the numerical variable you
chose above.
(c) Say you want to test the hypothesis that the mean tail length of the sample of
finches is different from 44 mm. List the corresponding null and alternative
(d) Evaluate your hypothesis test using a level of confidence α = 0.05.
(e) Does your confidence interval match the conclusion from your hypothesis test?
(f) What does the confidence interval tell you that the hypothesis test does not?
(g) Describe at least three things about 4th observation in the data set (using the information provided by the other variables for that observation, such as ”beaklength”).



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