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WorksheetsFinal Exam for Probability and Statistics
Total questions: 60
Worksheet time: 42mins
The null and alternative hypothesis are statements about the significant difference between
parameter and statistic
parameter and sample size
population size and statistic
mean and standard deviation
Which of the following does not describe an alternative hypothesis?
It is a hypothesis that has a statement of equality.
It is a hypothesis that has a statement of inequality.
It states a specific difference between a parameter and a statistic.
It states that there is a difference between a parameter and a statistic.
Which of the following does not describe a null hypothesis?
It is denoted by Ho.
It is the hypothesis to be tested.
It has a statement of equality.
It states a specific difference between a parameter and a statistic.
What does level of significance mean in a hypothesis testing?
Probability of calculating the hypothesized mean
Probability of not rejecting the null hypothesis when it is false
Probability of not calculating the hypothesized mean
Probability of rejecting the null hypothesis when it is true
If the alternative hypothesis containes the symbol ">", where is the rejection region located?
Center region
Left end tail region
Right end tail region
Both end tail regions
A teacher claims that the mean math svore of all grade 11 students is 90. Where is the rejection region located?
Center region
Left end tail region
Right end tail region
Each end tail regions
What is the probability of rejecting the null hypothesis of a left-tailed test given the level of significance alpha=0.01?
0.01
0.05
0.001
0.005
Mr. Mojica claimed that his operators could finish their work in less than three hours. Which is the correct set of hypotheses to test his belief?
Ho: u < or = 3; Ha: u > 3
Ho: u > 3; Ha: u < 3
Ho: u > or = 3; Ha: u < 3
Ho: u = 3; Ha: u is not = to 3
A group of researchers wants to test the truth in the company's claim that the travel time from Magallanes to Manila takes an average of two hours. What are the possible Type I and Type II errors?
Type I error will occur if the actual average travel time is two hours by Ho is rejected. Type II error will occur if the actual average travel time is not two hours but Ho is not rejected.
Type I error will occur if the actual average travel time is two hours by Ho is not rejected. Type II error will occur if the actual average travel time is not two hours but Ho is not rejected.
Type I error will occur if the actual average travel time is two hours by Ho is not rejected. Type II error will occur if the actual average travel time is not two hours but Ho is rejected.
Type I error will occur if the actual average travel time is two hours by Ho is rejected. Type II error will occur if the actual average travel time is not two hours but Ho is rejected.
What corresponding value will be calculated when the t-test statistic is computed?
Hypothesized population mean
Hypothesized sample mean
Standardized t-value
Standardized z-value
A left-tailed test with 1% level.of significance has a z-critical value of -2.33. What is the appropriate decision rule?
Reject Ho if the calculated test statistic z-value is greater than 2.33.
Reject Ho if the calculated test statistic z-value is less than -2.33.
Reject Ho if the calculated test statistic z-value is less than -2.33.
Reject Ho if the calculated test statistic z-value is greater than -2.33.
Given a right-tailed test, if the calculated test statistic t-value is less than the critical value t alpha, the null hypothesis is
Not accepted
Rejected
Not rejected
Not enough information
Which of the following is not included in the hypothesis testing procedure?
Compute the test statistic.
Decide whether to reject the null hypothesis.
Select a level of significance for Beta.
State the null and alternative hypothesis.
A soft drink vending machine is adjusted so thay on average, it will automatically dispense 200 mL into a paper cup however, the actual dispensed is not exactly 200 mL. The operation manager obtains a sample of 35 cups of dispensed soda and the mean of his sample is 195 mL. The machine operates with a known standard deviation of 14 mL. At 5% level of significance, what isbyhe appropriate decision rule?
Reject Ho if the test value is less than -1.96 or is greater than 1.96.
Do not reject Ho if the test value is equal to -1.96.
Reject Ho if the test value is greater than -1.96 or is less than 1.96.
Do not reject Ho if the test value is equal go 1.96.
What statistical test is appropriate to use in hypothesis testing if the distribution is normally distributed, the samole size is less than 30, and the population standard deviation is unknown?
Alternative test
Hypothesis test
t-test
z-test
What statistical test is appropriate to use in hypothesis testing if the distribution is normally distributed, the samole size is greater than 30, and the population standard variance is known?
Alternative test
Hypothesis test
t-test
z-test
In t-test, if the population standard deviation is unknown, what can be used to replace the population standard deviation?
Sample standard deviation
Sample size
Hypothesis standard deviation
Population variance
If you are using a t-test statistic in hypothesis testing, what must be assumed about the distribution of the data?
Not normally distributed
Normally or approximately normally disttibuted
Right tailed distribution
Left tailed distribution
What formula for test statistic is appropriate to use if the sample size is greater than or equal to 30 and the population standard deviation is unknown?
What formula for test statistic is appropriate to use if the sample size is less than 30 and the population variance is unknown?
The hypothesized population mean is to be tested. The population has a standard deviation of 3. A sample size of 60 is used with a mean of 12.5. Assuming that the underlying population is normally distributed, what test statistic should be used to perform the hypothesis test?
t-value
z-value
t-test
z-test
An accounting firm claimed that the average entry level salary of accountants in Dasmariñas City is P18,000 per month. It was believed that this is not true, so a random sample of 25 entry level accountants was studied and found that tge average salary is P19,000 with a variance of P1,000. Determine the appropriate test statistic.
t-value
z-value
t-test
z-test
A normally distributed standardized English test is known to have a mean score of 73 and a standard deviation of 10. The test is given 40 sophomore students and the class mean is 76. Using 1% level of significance, test if the population average is not 73.
There is sufficient evidence to claim that, at 1% level.of significance, the mean score of the population is 73.
There is no sufficient evidence to claim that, at 1% level of significance, the mean score is 76.
There is sufficient evidence to claim that, at 1% level of significance, the mean score is 76.
There is no sufficient evidence to claim that, at 1% level of significance, the mean score of the population is not 73.
A laptop manufacturer claims that the latest model of laptop will last an average of 10 hours under normal use. A researcher randomly selects 25 laptops of the latest model from the company and tested these laptops. The selected laptops have a mean lifespan of 8.5 hours and a standard deviation of 3.7 hours. Does the company have enough evidence that their claim is true at 1% level of significance?
There is insufficient evidence to claim that the latest laptop model will last an average of less than 10 hours under normal use.
There is sufficient evidence to claim that the latest laptop model will last an average of 10 hours under normal use.
There is sufficient evidence to claim that the latest laptop model will not last for 10 hours under normal use.
There is insufficient evidence to claim that the latest laptop model will last an average of 10 hours under normal use.
How many rejection regions does a two-tailed test have?
One
Two
Three
None
If the alternative hypothesis contains the "<" symbol, where is the rejection region located?
Left end tail region
Center
Both end tail regions
Right end tail region
Assume the null hypothesis states that the mean is at most 20. A sample size of 25 with mean and standard deviation equal to 22 and 5.35 respectively, is taken from the population. Using 0.10 level of significance, what is the critical value and the probability of the rejection region?
The critical value is -1.318 and the probability of the rejection region is 0.10.
The critical value is -1.318 and the probability of the rejection region is 0.05.
The critical value is 1.318 and the probability of the rejection region is 0.05.
The critical value is 1.318 and the probability of the rejection region is 0.10.
The p-value in hypothesis testing represents which of the following: please select the best answer below.
The probability of failing to reject the null hypothesis, given the observed results.
The probability that the null hypothesis is true, given the observed results.
The probability that the obsereved results are statistically significant, given the null hypothesis is true.
The probability of observing results as extteme or more extreme than currently observed, given that the null hypothesis is true.
Assume that the cholesterol levels in a certain population have a mean pf 200 and a standard deviation of 24. The cholesterol levela for a random sample of 9 individuals are measured and the sample mean X is determined. What is the z-score for a sample mean of 180?
-3.75
-2.50
-0.83
2.50
A result is "statistically significant" whenever
The null hypothesis is true.
The alternative hypothesis is true.
The p-value is less than or equal to the significance level.
The p-value is larger than the significance level.
One problem with the hypothesis testing is that a real effect may not be detected. The problem is most likely occur when
The effect is small and the sample size is small.
The effect is large and the sample size is small.
The effect ia small and the sample size is large.
The effect is large and the sample size is large.
Which of the following statements about the Central Limit Theorem is correct?
The CLT states that the sample mean is always equal to the population mean.
The CLT states that the samoling distribution of the sample mean is approximately normal for large sample sizes n > 30.
The CLT states that the sample mean is equal to the population mean, provided that n > 30.
The CLT states that the sampling distribution of the population mean is approximately normal, provided that n > 30.
A house cleaning service claims that it can clean a four-bedroom house is less than 2 hours. A sample of n = 36 houses is taken and the sample mean is found to be 1.97 hours and the sample standard deviation is found to be 0.1 hours. Using a 0.05 level of significance, the conclusion is:
Reject the null because the test statistic (-1.8) is < the critical value (-1.64).
Do not reject the null because the test statistic (-1.8) is < the critical value (-1.64).
Reject the null because the test statistic (-1.8) is > the critical value (-1.96).
Do not reject the null because the test statistic (-1.8) is > the critical value (-1.96).
A hypothesis test is done in which the alternative hypothesis is more than 10% of a population is left handed. The p-value for the test is calculated to be 0.25. Which statement is correct?
We can conclude that more than 10% of the population is left-handed.
We can conclude that more than 25% of the population is left-handed.
We can conclude that exactly 25% of the population is left-handed.
We cannot conclude that more than 10% of the population is left-handed.
As the degrees of freedom for the t-distribution increases, the distribution approaches
value of zero for the mean.
the t-distribution.
the normal distribution.
the binomial distribution.
Which of the following is not true about the hypothesis tests?
Hypothesis test are only valid when the sample is representative of the population for the question of interest.
Hypotheses arr statements about the population represented by the samples.
Hypotheses are statements about the sample (or samples) from the population.
Conclusions are statements about the population represented by the samples.
A statement made about a population for testing purpose is called
Statistic
Hypothesis
Level of significance
Test statistic
If the assumed hypothesis is tested for rejection considering it to be true, then it is called
Null hypothesis
Statistical hypothesis
Simple hypothesis
Composite hypothesis
A statement whose validity is tested on the basis of a sample is called
Null hypothesis
Statistical hypothesis
Simple hypothesis
Compoaite hypothesis
A hypothesis which defines the population distribution is called
Null hypothesis
Statistical hypothesis
Simple hypothesis
Altenative hypothesis
The point where the null hypothesis gets rejected is called
Significant value
Rejection value
Acceptance value
Critical value
The type of test is defined by which ofnthe following?
Null hypothesis
Alternative hypothesis
Simple hypothesis
Compoaite hypothesis
Which of the following is defined as the rule or formula to test a null hypothesis?
Test statistic
Population statistic
Variance statistic
Null statistic
Alternative hypothesis is also called as
Composite hypothesis
Research hypothesis
Simple hypothesis
Null hypothesis
What is the mean of a Chi Square distribution with 6 degrees of freedom?
4
12
6
8
Which Chi Square diatribution looks the most like a normal distribution?
A Chi Square distribution with 4 degrees of freedom.
A Chi Square distribution with 8 degrees of freedom.
A Chi Square distribution with 12 degrees of freedom.
A Chi Square distribution with 16 degrees of freedom.
A sample size is considered large in which of the following cases.
n > or = 30
n > or = 50
n < or = 30
n < or = 50
What typenof test is to be used in the hypothesis: the average monthly income of a domestic helper in the city of Dasmariñas is P8,000?
Two-tailed test will be used because the alternative hypothesis is non-directional. (= or not equal to)
Right-tailed test will be used because the alternative hypothesis is directional. (>)
Left-tailed test will be used because the alternative hypothesis is directional. (<)
Right-tailed test will be used because the alternative hypothesis is directional. (<)
It is a plot of pairs of values in a rectangular coordinate plane displaying a relationship between two variables.
Bar graph
Histogram
Pie chart
Scatter plot
It is an unusual observation that is extremely high or extremely low. It is a point that is far from the cluster of points.
Coefficient of determination
Midpoint
Outlier
Pearson r
It is a measure that gives the proportion of total variability in the dependent variable y that could be explained or accounted bybthe linear relationship with the independent variable x.
Coefficient of determination
Midpoint
Outlier
Pearson r
Determine the coefficient of determination between mileage and the price of used vans if the correlation coefficient is -0.994.
96.60%
97.70%
98.80%
99.90%
Which of the following is not a property of the sample correlation coefficient?
The sample correlation coefficient r is always between -1 and 1.
A positive value of r means a direct relationship between two variables.
A negative value of r meana an inverse relationship between two variables.
The closer the value of r to 1 or -1, the stronger the linear relationahip between two variables is.
None of the these.
Which of the followingnstatement is false?
Correlation is positive when y increases as x increases.
Correlation is negative when y decreases as x increases.
A correlation coefficient of 0 means thee is no linear relationahip between two variables.
A correlation coefficient of -1 means perfect positive linear relationship between two variables.
Calculate the correlation coefficient r between the variables.
0.9517
0.9617
0.9671
0.9716
What are the coefficients of the estimates regression line y = bx + a?
b = 0.69434 and a = 28.55288
b = 0.71243 and a = 28.52475
b = 0.70343 and a = 29.55882
b = 0.70345 and a = 29.55885
Determine the simple linear regression equation of the data in the table.
y = 0.69434x + 28.55288
y = 0.70345x + 29.55885
y = 0.71243x + 28.52475
y = 0.70343x + 29.55882
Which of the following best illustrates the data?
Which of the following best illustrates the 'line of best fit' for the scatter plot?
Which of the following shows the best 'line of best fit' for the scatter plot diagram?
