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In 1970, 36% of first year college students thought that being "very well off financially is very important or essential." By 2000 the percentage had increased up to 74%. These percentages are based on nationwide multistage cluster samples.
a) Is the difference important? Or does teh question make sense?
b) Does it make sense to ask if the difference is statisically significante? Can you answer on the basis of the informations given?
c) Repeat b), assuming the percentages are based on independant simple random samples of 1,000 first year college students drawn each year.

Respuesta :

Answer:

a.  The difference is important but the question does not make sense

b. Yes, it makes sense to ask if the difference is statistically significant.

c. Please check explanation

Step-by-step explanation:

From the question, we identify the following relation;

[tex]H_{o}[/tex]: [tex]P-P_{1}[/tex] = 0

[tex]H_{A}[/tex] : [tex]P-P_{1}[/tex] ≠ 0

a) The difference is important as asked, but the cultural atmosphere difference of over 30 years makes the question somehow not making sense

b) Yes, it makes sense. In order to answer, it is necessary to know the sample size of the year  2000 survey.

We can answer the question on the basis of the information given.

c) We proceed here as follows;

α = 0.05 , [tex]Z_{alpha/2}[/tex] = 1.96 ( This is the critical value)

Thus, z = (0.74-0.36)/√(0.36-0.64)/1000 = 25.03

We make the following conclusions; Since 25.03 > 1.96, the null hypothesis[tex]H_{o}[/tex]  is rejected which means that the proportion of people who think being well officially is important has changed since 1970.

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