A type I error is the mistake of rejecting the null

A type I error is the mistake of rejecting the null

Subject: Mathematics    / Statistics
Question

State whether the following statements are True or False. (6 marks, 1
Mark Each)
1. A type I error is the mistake of rejecting the null
hypothesis when it is actually false.
2. Two samples are independent if the sample values
selected from one population are not related to the
sample values from the other population.
3. The null hypothesis (denoted by H0) is a statement that
the value of a population parameter is equal to some
value.
4. In case of hypothesis testing for a sample, the t statistic
is used if ? is not known and sample size n is greater
than 5 (n>5)
5. A claim that two population proportions are equal, each
of the two samples must satisfy the requirement that
np ? 30 and nq ? 30 .
6. In an unpaired samples t-test with sample sizes n1= 21
and n2= 11, the value of t should be obtained at 32
degree of freedom.

(Multiple Choice Questions)
1 Mark Each)
1. If p-value < ?, then
A. Reject H0
B. Accept H0
C. Reject H1
D. All the above 2. (6 marks, The MEAN of the Student t_distribution is
A. equal to 0
B. less than 1
C. less than 0
D. greater than 1 3. A decision in a hypothesis test can be made by using a :
1. P-value 2. Critical Value
3. A and B
4. None of the above
4. When carrying out a large sample test of H 0: ?0 = 10
vs. H: ?0 > 10 by using a rejection point, we reject H 0
at level of significance ?
when the calculated test
statistic is:
1. Less than z ?
2. Less than – z ?
3. Greater than z ? / 2
4. Greater than z ?
5. A randomly selected sample of 500 college students
was asked whether they had ever used the drug
Ecstasy. Sixteen percent (16% or 0.16) of the 500
students surveyed said they had. Which one of the
following statements about the number 0.16 is correct?
A. It is a population proportion.
B. It is a margin of error.
C. It is a sample proportion.
D. It is a randomly chosen number.
6. Sample sizes n1 = 100, n2 = 100 and numbers x1 =
39, x2 = 41 of successes to find the pooled estimate
´p 1.
2.
3.
4. 0.4
0.8
0.36
0.48 Part-II (Multiple Choice Questions)
Mark Each)
MCQ
1
2
3
4
5
Answe
rs (6 marks, 1
6

Section –III
Answer the following Essay Type Questions (18 marks, 3 Mark Each)
1. Suppose the national unemployment rate is 3%. In a
survey of n = 450 people in a rural Wisconsin county,
22 people are found to be unemployed. County
officials apply for state aid based on the claim that the
local unemployment rate is higher than the national
average. Test this claim at the .05 significance level.
2. Suppose we would like to determine if the typical
amount spent per customer for dinner at a new
restaurant in town is more than $20.00. A sample of
49 customers over a three-week period was randomly
selected and the average amount spent was $22.60.
Assume that the standard deviation is known to be
$7.50. Using a 0.05 level of significance, would we
conclude the typical amount spent per customer is
more than $20.00?
3. The scores on an aptitude test required for entry into a
certain job position have a mean at most 500. If a
random sample of 36 applicants have a mean of 546
and a standard deviation of 120, is there evidence that
their mean score is different from the mean that is
expected from all applicants?. Use a 0.05 level of
significance.
4. The table show the number satisfied in their work in a sample of working adults with a college education and in
a sample of working adults without a college education.
Do the data provide sufficient evidence that a greater
proportion of those with a college education are satisfied
in their work? Use a significance level of ? = 0.05 to test
the claim that p1 < p2. Number satisfied in
their work
Number in sample College Education
12 No College Education
27 46 43 Q. 5 & 6.Use the following information to answer
Questions 5 and 6:
Given the following data of two independent samples
of normally distributed populations Dat
a Populatio
n1 Populatio
n2 n 23 13 43 41 4.5 5.1 ´x s A. Test the claim that ?1 ? ?2 at the ?=0.05 level of
significance
B. Construct a 95% confidence interval about
?1??2 .