Basic Statistics Week 8 Final Exam Quiz Answer
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Statistics Week 8 Final Exam Quiz Answer with you..
Basic Statistics Final Exam
Question 1)
What does the test statistic tell you?
- It's another word for the p-value.
- It indicates whether you should use z- or t-distribution to calculate probability.
- It indicates how far from the actual population value your sample mean lies.
- It indicates how many standard errors a point estimate lies from the expected null hypothesis population value.
Question 2)
In a group of students 25% are enrolled in physics, 23% in sociology,
17% in chemistry, 14% in political science, 12% in anthropology, and 9%
in math. You are going to select an individual from the group of
students. The probability of event A is equivalent to the probability
that you select someone who studies social science (sociology, political
science and anthropology) or physics. What is the probability of the
event A’s complement?
- 0.51
- 0.26
- 0.49
- 0.74
Question 3)
Assume your null hypothesis is μ = 6. In your sample you find a value
that is lower than 6. Is it 'easier' to reject the null hypothesis with
a one-tailed or two-tailed test?
- A one-tailed test.
- A two-tailed test.
- This depends on the P value.
- This depends on the level of significance.
Question 4)
Someone makes the following assertion: if the sample becomes larger,
then the standard deviation becomes smaller. Which of the following
statements is correct?
- This assertion does not apply to any distribution.
- This assertion always applies to all distributions.
- This assertion always applies to the sampling distribution.
- This assertion always applies to the sample distribution and the sampling distribution.
Question 5)
The largest number of Oscars received by a film in year X was 4. This
was different in previous years. Below is a probability distribution for
the number of Oscars per Oscar winning film. What is the standard
deviation of this distribution?
- 1.82
- 1.19
- 6
- 1.32
Question 6)
You draw a sample from the population of a town (n = 312) and find
that of this sample, 23% are highly educated and 27% are low-educated.
What is the 80% confidence interval for the proportion of highly
educated people in this town?
- (0.21, 0.25)
- (0.20, 0.26)
- (0.25, 0.29)
- (0.23, 0.27)
Question 7)
What type of table is shown below?
- Data matrix
- Cross table
- Scatterplot
- Frequency table
Question 8)
You know that there is a strong correlation between the consumption
of ice cream and body weight. The Pearson's r = 0.78. You also know
that the average consumption of ice cream per week is five grams with
a standard deviation of 1.5 grams. The average weight is 65 kg with a
standard deviation of 15 kg. What is the formula of the regression
line?
- ŷ = 26 + 7.8x
- ŷ = 7.8 + 26x
- ŷ = -502 + 0.078x
- ŷ = 0.078 - 502x
Question 9)
See the sample space below. What is the probability of event B
occurring, given that event A has occurred?
- 0.82
- 0.19
- 0.09
- 0.23
Question 10)
What is a probability?
- A P-value.
- An uncertainty.
- The number of times that something occurs in an experiment.
- The proportion of times that something will occur in the long run.
Question 11)
25% of all students find this BS exam difficult. You select four random students. What is the probability
that exactly two of them find this exam difficult?
- 0.06
- 0.07
- 0.21
- 0.02
Question 12)
Various forms of bias can occur when we select a sample. What is
sampling bias?
- If not everyone in the sample belongs to the population.
- If not everyone in the sample actually participates in the research.
- If not everyone in the sampling frame has an equal chance to get into the sample.
- If not everyone in the population has an equal chance to enter the sampling frame.
Question 13)
Variable A is normally distributed with μ = 12.30 and σ = 3.11.
What is the probability that a randomly selected case will have a
score of less than 14?
- 0.88
- 0.29
- 0.71
- 0.12
Question 14)
A random sample of 61 Basic Statistics students were asked what they
thought of statistics on a scale of 0 (very stupid) to 100 (very
nice). Interestingly, students seem to find statistics quite nice: the
sample mean equals 83. The sample standard deviation equals 7. We know
that the standard deviation in the population (all BS students) is 8.
Calculate the 90% confidence interval.
- (81.53, 84.47)
- (81.24, 84.76)
- (81.32, 84.68)
- (80.99, 85.01)
Question 15)
You know that for variable A μ = 1400 and σ = 300. You also know that the variable is normally distributed. You decide to change
the scores of this variable into z-scores. What is the mean and
standard deviation of this new distribution?
- Mean = 0, standard deviation = 1.
- Mean = 1400, standard deviation = 300.
- Mean = 1400, standard deviation = 1.
- Cannot be calculated on the basis of this information.
Question 16)
Ten students resit the Basic Statistics exam. Their final grades are:
4, 4, 2, 9, 7, 9, 6, 4, 7, 8. What is the interquartile range?
- 2
- 8
- 4
- 7
Question 17)
Which of the following is not the explained variance?
- The percentage of variance in Y that is explained by the mean of X.
- The degree to which the regression equation of X and Y is better at predicting the dependent variable than the average of Y.
- The percentage of the variance in Y which is explained with the regression equation.
- The Pearson r squared.
Question 18)
Look at the following cross table of two ordinal variables. Is there
a correlation between variable A and B?
- Cannot be seen from the table.
- Yes, there is a positive correlation.
- Yes, there is a negative correlation.
- No, there is no correlation.
Question 19)
Look at the table below. Calculate the Pearson's r.
- 0.81
- 0.61
- 0.71
- 0.91
Question 20)
Based on a random sample of n = 2345, the 95% confidence interval of
variable X is (7.25, 9.12). You expect that the mean in the population
is different from 7 at α = 0.05. What can you conclude?
- You cannot reject the null hypothesis.
- This confidence interval is wrong.
- Nothing, because you have not enough data to determine that.
- The value in the population is indeed different from 7.
Question 21)
Which of the following statements about the regression line is not
correct?
- The regression line can run horizontally.
- The constant indicates the place where the regression line crosses the Y-axis.
- The regression line is the line of which the sum of the residuals is the smallest.
- The regression coefficient is the change in the Y value with 1 unit increase in the X value.
Question 22)
You’re going to draw a random sample of professional football players
because you want to know what percentage have completed high school.
You want to have a margin of error of up to 0.03 at a confidence level
of 90%. How big should your sample be?
- At least 30
- Minimum 1068
- Minimum 456
- Minimum 748
Question 23)
81 random elementary schools were asked for their average exam scores
(sample mean = 535, sample standard deviation = 7). Calculate the 98%
confidence interval.
- (533.41, 536.59)
- (528.00, 542.00)
- (533.15, 536.85)
- Not possible to calculate based on this information.
Question 24)
A type I error means that:
- The null hypothesis is true, and you reject the null hypothesis.
- The null hypothesis is false, and you reject the null hypothesis.
- The null hypothesis is false and cannot reject the null hypothesis.
- The null hypothesis is true, and you do not reject the null hypothesis.
Question 25)
You know that the heights of four people are: 156 cm, 184 cm, 172 cm
and 165 cm. What is the standard deviation?
- 28
- 10.23
- 139.58
- 11.81
Question 26)
Last year the mean turnover of a group of companies was 434,000 euro.
You have good reasons to expect that this year’s turnover will be
higher. Your null hypothesis is therefore: μ = 434,000. Your
alternative hypothesis is: μ > 434,000.
You randomly sample 101 companies from the population. The sample
mean turns out to be 450,000 euro, with a standard deviation of
100,000 euro. Calculate the test statistic. Which of the following
statements is correct?
- You reject the null hypothesis at both α = 0.05 and α = 0.10.
- You reject the null hypothesis at α = 0.05, but not at α = 0.10.
- You reject the null hypothesis at α = 0.10, but not at α = 0.05.
- You do not reject the null hypothesis at α = 0.05, and not at α = 0.10.
Question 27)
Film critics gave the film Basic Statistics: The Movie an average
rating of 8.1 (on a scale of 0-10). The standard deviation is 0.7. You
drew a random sample of n = 56 from all film critics and asked them to
rate the film Basic Statistics: The Movie with a number. What is the
probability that the average rating in the sample is greater than
8.0?
- 14%
- 44%
- 86%
- 56%
Question 28)
You draw a sample from the population of Dutch voters. You do this by
randomly selecting 10 voters from each municipality. What kind of
sample is this?
- Snowball
- Convenience
- Cluster random
- Stratified random
Question 29)
What does the 95% confidence interval tell us?
In 95% of cases when we sample from a population, the sample mean falls
within the interval:
sample mean ± 1.96 * standard deviation of the sampling distribution.
In 95% of cases when we sample from a population, the sample mean falls
within the interval:
sample mean ± 1.64 * standard deviation of the sampling
distribution.
In 95% of cases when we sample from a population, the population mean
falls within the interval:
sample mean ± 1.96 * standard deviation of the sampling
distribution.
In 95% of cases when we sample from a population, the population mean
falls within the interval:
sample mean ± 1.64 * standard deviation of the sampling distribution.
Question 30)
What is a characteristic of the t-distribution?
- The t distribution has a mean of one.
- The t-distribution has the same shape as the normal distribution.
- A t-value that is multiplied with a standard error is equal to the margin of error for a confidence interval of a mean.
- The t-distribution approaches the normal distribution if it has a large standard deviation.
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