Statistics

1. Answer the following questions using sheet Population which contains data taken from a population of 536 individuals who completed a survey about their expenditure. It contains data on weekly clothing expenditure (£/week). The spreadsheet also contains data on the gender of the individual. Assume expenditure is normally distributed.

a) What is the mean value of weekly clothing expenditure? Interpret this value.

b) What are variance and standard deviation of clothing expenditure for the population?

c) What is the mean clothing expenditure for males? and for females? Compare and interpret the

two values.

If a random sample of size n=100 is drawn from the population:

d) Calculate the standard error of the sample mean for clothing expenditure

STUDENT ID:

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e) Calculate the two limits within which 95% of the sample means will fall, clearly showing the critical value and ALL relevant information. Interpret this interval.

f) Showing method, calculate the probability of getting a sample mean above £22?

The sheet Sample1 contains a large sample of 70 individuals taken from the population. Assume that you do not know the population mean or standard deviation.

g) What is the mean value of clothing expenditure for the sample?

h) What are variance and standard deviation of clothing expenditure for the sample?

i) Calculate the standard error of the sample mean.

j) Write the null and alternative hypotheses to test whether average weekly expenditure is less than £25.

k) What is the appropriate test to perform and why?

l) Calculate the test statistic.

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m) Find, using excel or the probability tables, the critical value for the test if a=0.05 showing

ALL relevant information

n) What is your decision and conclusion regarding the null and alternative hypotheses?

o) What is the p-value of the test?

p) Sketch the distribution showing the test statistic, critcal value, the rejection region for the test and the p-value.

The sheet Sample 2 contains a small sample of 28 individuals taken from the population. Assume

that you do not know the population mean or standard deviation.

q) What are the mean values of clothing expenditure for males? and for females?

r) What are the sample standard deviations of expenditure for males and for females. (Hint: if you

haven’t already done so, sort the data by gender)

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s) Calculate the standard error of the difference in means.

t) Calculate a 90% confidence for the difference in means between females and males, clearly

showing the critical value and ALL relevant information. Interpret the confidence interval.

u) You should have found that the difference in sample means between female and male spending

is almost £20 but your confidence interval is not able to suggest that the difference in population

means ismore than £10. Why do you think the interval is so wide?

v) Write the null and alternative hypotheses to test whether expenditure by females is greater than

£5 more than expenditure by males.

w) Calculate the test statistic.

x) Find, using excel, the p-value for the test showing ALL relevant information

y) What is your decision and conclusion regarding the null and alternative hypotheses at the 5%

significance level?

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