In the last presidential campaign, Bernie kept making the claim that the average

Question

In the last presidential campaign, Bernie kept making the claim that the average donation to his campaign was $27. You have kept a record of the 11 donations for your candidate over the past six days; they are listed below.

Donations: 55 40 20 35 350 27 17 18 18 18 45

Calculate the standard deviation and three measures of central tendency for these data. Is Bernie's claim accurate? Which of the measures of central tendency would give your candidate the most accurate estimate of the week's donations?

Explanation / Answer

The measures of central tendency are as follows:

xbar=summation x/n=(55+40+...+45)/11=643/11=$58.5

Arrange the data in ascending order, 17, 18, 18, 18, 20, 27, 35, 40, 45, 55, 350

For odd numbered data (n=11), the median is the middlemost number. Therefore, median, M=27.

Mode: 18 (number of occurence: 3)

The distribution is right skewed, hence, median gives the most accurat emeasure of central tendency.

Standard deviation, s=sqrt[1/n-1 summation (x-xbar)^2]=sqrt[1/11-1 {(55-58.5)^2+...+(45-58.5)^2]=$97.6

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Hypotheses to test Bernie's claim are as follows:

H0:mu=27 (average donation to his campaign is $27)

H1:mu=/=27 (average donation to his campaign is different from $27)

For samll sample size, n<30 and unknown population standard deviation, calculate t test statistic.

t=(xbar-mu)/(s/sqrt n), where, xbar is sample mean, mu is population mean, s is sample standard eviation and n is sample size.

=1.07

p value at 10 df [df=n-1] is 0.310. Per rejection rule based on p value reject H0 if p value is less than alpha=0.05. Here, 0.310 is not less than 0.05, therefore, fail to reject H0. Insufficient sample evidence to conclude that  average donation to his campaign is different from $27.

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