Researchers interviewed street prostitutes in Canada and the United States. The mean age of the 100 Canadian prostitutes upon entering prostitution was 18 with a standard deviation of seven. The mean age of the 130 United States prostitutes upon entering prostitution was 20 with a standard deviation of nine. Is the mean age of entering prostitution in Canada lower than the mean age in the United States? Test at a 1% significance level. NOTE: If you are using a Student's t- distribution for the problem, including for paired data, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.) c) In words, state what your random variable d) State the distribution to use for the test. (Enter your answer in the form z or tdf where df is the degrees of freedom. Round your answer to two decimal places.) e) What is the test statistic? (If using the z distribution round your answer to two decimal places, and if using the t distribution round your answer to three decimal places.) f) What is the p-value? ( Round your answer to four decimal places.) Explain what the p-value means for this problem. g) Sketch a picture of this situation. Label and scale the horizontal axis and shade the region(s) corresponding to the p- value. h) Indicate the correct decision ("reject" or "do not reject" the null hypothesis), the reason for it, and write an appropriate conclusion. i) Explain how you determined which distribution to use.
Researchers interviewed street prostitutes in Canada and the United States. The mean age of the 100 Canadian prostitutes upon entering prostitution was 18 with a standard deviation of seven. The mean age of the 130 United States prostitutes upon entering prostitution was 20 with a standard deviation of nine. Is the mean age of entering prostitution in Canada lower than the mean age in the United States? Test at a 1% significance level. NOTE: If you are using a Student's t- distribution for the problem, including for paired data, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.) c) In words, state what your random variable d) State the distribution to use for the test. (Enter your answer in the form z or tdf where df is the degrees of freedom. Round your answer to two decimal places.) e) What is the test statistic? (If using the z distribution round your answer to two decimal places, and if using the t distribution round your answer to three decimal places.) f) What is the p-value? ( Round your answer to four decimal places.) Explain what the p-value means for this problem. g) Sketch a picture of this situation. Label and scale the horizontal axis and shade the region(s) corresponding to the p- value. h) Indicate the correct decision ("reject" or "do not reject" the null hypothesis), the reason for it, and write an appropriate conclusion. i) Explain how you determined which distribution to use.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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Transcribed Image Text:Researchers interviewed street prostitutes in Canada
and the United States. The mean age of the 100
Canadian prostitutes upon entering prostitution was 18
with a standard deviation of seven. The mean age of
the 130 United States prostitutes upon entering
prostitution was 20 with a standard deviation of nine. Is
the mean age of entering prostitution in Canada lower
than the mean age in the United States? Test at a 1%
significance level. NOTE: If you are using a Student's t-
distribution for the problem, including for paired data,
you may assume that the underlying population is
normally distributed. (In general, you must first prove
that assumption, though.) c) In words, state what your
random variable d) State the distribution to use for the
test. (Enter your answer in the form z or tdf where df is
the degrees of freedom. Round your answer to two
decimal places.) e) What is the test statistic? (If using
the z distribution round your answer to two decimal
places, and if using the t distribution round your answer
to three decimal places.) f) What is the p-value? (
Round your answer to four decimal places.) Explain
what the p-value means for this problem. g) Sketch a
picture of this situation. Label and scale the horizontal
axis and shade the region(s) corresponding to the p-
value. h) Indicate the correct decision ("reject" or "do
not reject" the null hypothesis), the reason for it, and
write an appropriate conclusion. i) Explain how you
determined which distribution to use.
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