The Comrades committee decided to investigate the age (in years) of male and female runners. The descriptive statistics obtained from the two independent samples are recorded in the table below. Male runners Female runners Sample Size n1=12 n2=16 Sample Mean x¯1=34.75 x¯2=30.56 Sample Standard Deviation s1=8.114 s2=6.387 Research question: The Comrades committee would like to investigate whether the average age of male and female runners differ significantly from each other at an α=0.1 level of significance. Let: μ1= average age of male Comrades runners μ2= average age of female Comrades runners Given: The age of the male and female runners are normally distributed with unequal variances. Under the null hypothesis, the test statistic has a t distribution with 20 degrees of freedom, i.e. t∼t20 a) The point estimate of (μ1−μ2) is (Round answer to 2 decimal places) If we can draw the conclusion that, on average, the male runners are older than the female runners, then we can also conclude that (μ1−μ2) is significantly (select one from options): less than 4.19 different from 0 less than 0 different from 4.19 more than 0 more than 4.19 b) Calculate the value of the test statistic. (Round answer to 4 decimal places) c) Decision and conclusion: The Comrades committee will reject the null hypothesis if t≤ or if t≥ and consequently make the conclusion that the average age of males and females (differ/do not differ) significantly from each other. A 90% confidence interval to support this decision is ( _ ; _____ )

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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a) The point estimate of (μ1−μ2) is ______ (Round answer to 2 decimal places)

If we can draw the conclusion that, on average, the male runners are older than the female runners, then we can also conclude that (μ1−μ2) is significantly (select one from options):

less than 4.19
different from 0
less than 0
different from 4.19
more than 0
more than 4.19

b) Calculate the value of the test statistic. __________(Round answer to 4 decimal places)

c) Decision and conclusion:

The Comrades committee will reject the null hypothesis if t≤ ________ or if t≥ ________ and consequently make the conclusion that the average age of males and females ________ (differ/do not differ) significantly from each other.

A 90% confidence interval to support this decision is

( _________ ; _________ )

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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