Question

1. New York wants to do a study to compare students at two different schools in the city to see if student’s feelings about college are influenced by their tuition. The city takes a sample of 100 students from Barnard college whose tuition is 60 thousand dollars a year and 200 from Lehman College whose tuition is 15 thousand dollars a year. The ask each student the same question “Do you feel that your college is worth the tuition you pay for it?”. The survey found that 80% of the students at Lehman college agreed with the statement, while only 70% of the students at Barnard college agreed with the statement. The City believes that the proportion of students at Barnard and Lehman who think college is worth the money they pay for should be the same. Please test this hypothesis and use an alpha of .05 for this study. Please answer the questions below. (points 10)
   1. What Is the null and alternative hypotheses of the study? (2)
   2. What are the requirements for using a normal distribution to solve this problem? List them below (2)
   3. What is the critical value for this distribution? (1)
   4. What is the pooled probability of success for the study? (1)
   5. What is the standard deviation? (1)
   6. What is the sample statistics for this distribution? (1)
   7. Do I reject or accept the null hypotheses in my example? Explain? (2)

Answer 1

ANSWER::

Given that:

The city takes a sample of 100 students from Barnard college whose tuition 60 thousand dollars a year and 200 from Lehman college whose tuition is 15 thousand dollars a year

a)

What I the null and alternative hypothesis of the study?

Taking Barnard College as Sample 1 and Lehman College as Sample 2:

: Null Hypothesis:

: Alternative Hypothesis:

b)

What are the requirements for using a normal distribution to solve this problem?

Requirements for normal distribution:

(i) The sampling method for each population is Simple Random Sampling

(ii) The samples are independent

(iii) Each sample includes at least 10 successes and 10 failures

(iv) Each population is at least 20 times as big as its sample.

c)

What is the critical value for this distribution?

= 0.05

One Tail - Left Side Test

From Table, critical Value of Z = - 1.645

d)

What is the pooled probability of success for the study?

f)

What is the sample statistics for this distribution?

Test statistic is given by:

g)

Do I reject or accept the null hypothesis in my example ?why?

Table of Area Under Standard Normal Curve gives area = 0.3686

So,

P - Value = 0.5 -0.3686 = 0.1314

Since P - Value = 0.1314 is greater than \alpha = 0.05, the difference is not significant.

Fail to reject null hypothesis.

So,

Correct option:

Do not reject null hypothesis in my example.

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