State whether the following statements are True or False. ( 6 marks , 1 Mark Eac
ID: 3314360 • Letter: S
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 true.
2-The null hypothesis is rejected if the P-value 0.05.
3-Two samples are dependent if the sample values are matched pairs.
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 30 .
5-A claim that two population proportions are equal, each of the two samples must satisfy the requirement that and .
6-The Student t distribution and the normal distribution are symmetric.
Section-II
(Multiple Choice Questions) (6 marks, 1 Mark Each)
1-Area of the rejection region depends on …
a.Size of
b.Size of
c.Test-Statistic.
d.Number of values
2-A randomly selected sample of 1000 college students was asked whether they had ever used the drug ecstasy. Sixteen percent 16% or 0.16) of the 1000 students surveyed said that they had. Which one of the following statements about the number 0.16 is correct?
a.It’s a sample proportion.
b.It’s a population proportion.
c.It’s a margin of error.
d.It’s a randomly chosen number.
3-A decision in a hypothesis test can be made by using a
a.P-value
b.Critical Value
c.A and B
d.None of the above
4-When carrying out a large sample test of H0: = 10 vs. Ha: > 10 by using a rejection point, we reject H0 at level of significance when the calculated test statistic is:
a.Less than
b.Less than -
c.Greater than
d.Greater than
5-Sample sizes n1 = 50, n2 = 50 and numbers x1 = 15, x2 = 5 of successes to find the pooled estimate
a.0.4
b.0.2
c.2.0
d.None of the above
Two teams of workers assemble automobile engines at a manufacturing plant in Michigan. A random sample of 145 assemblies from team 1 shows 130 acceptable assemblies. A similar random sample of 125 assemblies from team 2 shows 120 acceptable assemblies. The pooled proportion for acceptable assemblies is:
a.250/270
b.270/250
c.20/270
d.270/20
Part-II (Multiple Choice Questions) (6 marks, 1 Mark Each)
MCQ
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Answers
Section –III
Answer the following Essay Type Questions (18 marks, 3 Mark Each)
1-The Pew Research Center claims that more than 55% of American adults regularly watch a network news broadcast. You decide to test this claim and ask a random sample of 425 Americans whether they regularly watch a network news broadcast. Of the 425 Americans, 255 responded yes. At a = 0.05, is there enough evidence to support the claim?
2-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
3-Suppose a researcher believes that college faculty vote at a lower rate than college students. She collects data from 200 college faculty and 200 college students using simple random sampling. If 120 of the faculty and 150 of the students voted in the 2016 Presidential election, is there enough evidence at the 5% level of significance to support the researcher’s claim?
Use the following information to answer Questions question 4 and 5
Given the following data of two independent samples of normally distributed populations
Population 1
Population 2
4-Test the claim that at the =0.05 level of significance
5-Construct a 95% confidence interval about .
6- « Can a person control certain body functions if that person is trained in a program of biofeedback exercises? An experiment is conducted to show that blood pressure levels can be consciously reduced in people trained in this program. The blood pressure measurements (in millimeters of mercury) listed in the table below represent readings before and after biofeedback training of six subjects. » Do the data provide enough evidence to indicate that the mean blood pressure level decreases after training? Use = .05.
Before : 136.9 ; 201.4 ; 166.8 ; 150.0 ; 173.2 ; 169.3
After : 130.2 ; 180.7 ; 149.6 ; 153.2 ; 162.6 ; 160.1
MCQ
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Answers
Explanation / Answer
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1) A type I error is the mistake of rejecting the null hypothesis when it is actually true.
Ans: In statistical hypothesis testing, a type I error is the incorrect rejection of a true null hypothesis (also known as a "false positive" finding), while a type II error is incorrectly retaining a false null hypothesis (also known as a "false negative" finding).
True
2-The null hypothesis is rejected if the P-value 0.05.
Ans: If the P-value is less than (or equal to) ,reject the null hypothesis in favor of the alternative hypothesis. If the P-value is greater than , do not reject the null hypothesis. Not necessary that alpha is always 0.05.
If alpha is 0.05 then True, if not given then false
3-Two samples are dependent if the sample values are matched pairs.
Ans: True
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 30 .
Ans: If SD is not know, then t test is used
true but sample size doesn't matter when Population SD is unknown
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