STATISTICS AND PROBABILITY

Summative Test No.1 Score: ______

Directions: Read, analyze and understand each item carefully. Write the letter of the correct answer on the space provided
before each number.
___ 1. In statistics, it proposes that there is no difference between certain characteristics of a population.
A. Alternative hypothesis
B. Substitute hypothesis
C. Null hypothesis
D. Statistical hypothesis
___ 2. It is a position that states something is happening, a new theory is preferred instead of an old one.
A. Alternative hypothesis
B. Substitute hypothesis
C. Null hypothesis
D. Statistical hypothesis
___3. Which of the following is a description of the power of the test?
A. The probability of accepting the alternative hypothesis when it is true.
B. The probability of failing to accept the alternative hypothesis when it is true.
C. The probability of rejecting the null hypothesis when it is false.
D. None of the above
___ 4. The average July temperature in a region, historically, has been 74.5 oF. Perhaps it is higher now. What is the null
hypotheses of the statement?
A. Ho: μ ≠ 74.5oF
B. Ho: μ ≤ 74.5oF
C. Ho: μ ≥ 74.5oF
D. Ho: μ = 74.5oF
___ 5. When a new COVID19 Vaccine is created, the pharmaceutical company must subject it to testing
before receiving the necessary permission from the Food and Drug Administration (FDA) to market
the vaccine. Suppose the null hypotheses is “the vaccine is unsafe.” What is the Type II Error?
A. To conclude that the vaccine is safe when in fact, it is unsafe.
B. Not to conclude that the vaccine is safe when, in fact, it is safe.
C. To conclude that the vaccine is safe when, in fact, it is safe.
D. Not to conclude that the vaccine is unsafe when, in fact, it is unsafe.
___ 6. A statistics senior high teacher believes that fewer than 20% of KSHS students answered the online
examination through google forms. He surveys 84 of his students and finds that 11 answered the
online exam. An appropriate alternative hypothesis is:
A. p = 0.20
B. p > 0.20
C. p < 0.20
D. p ≤ 0.20

For items 7-11, consider the problem below.

The father of a senior high school student is listing down the expenses he will incur when he sends his daughter to the
university. At the university where he wants his daughter to study, he hears that the average tuition fee is at least
Php15,000 per semester. He wants to do a test of hypothesis. Suppose from a simple random sample of 16 students, a
sample mean of Php14,750 was obtained. Further, the variable of interest, which is the tuition fee in the university, is said
to be normally distributed with an assumed population variance equal to Php150,000 and level of significance 𝛼=4% 0𝑟
0.04.
___ 7. What is the appropriate null hypothesis?
A. The average tuition fee in the targeted university is at most Php15,000.
B. The average tuition fee in the targeted university is at least Php15, 000.
C. The average tuition fee in the targeted university is less than Php15,000.
D. The average tuition fee in the targeted university more than Php15,000.

___ 8. What will be the appropriate alternative hypothesis?

A. The average tuition fee in the targeted university is less Php15,000.
B. The average tuition fee in the targeted university is more than Php15,000.
C. The average tuition fee in the targeted university is at most Php15,000.
D. The average tuition fee in the targeted university is at least Php15,000.
___ 9. Identify the level of significance.
A. 0.4% B. 0.2 C. 0.3 D. 4%
___10. What kind of test will be used?
A. One-tailed test. B. Two-tailed test C. Three-tailed test D. No-tailed test
___ 11.What test statistic is to be used?
A. zc = 𝑥−𝜇𝑠√𝑛 B. tc = 𝑥−𝜇𝑠√𝑛 C. tc = 𝜇−𝑥𝜎√𝑛 D. zc = 𝑥−𝜇𝜎√𝑛
___12. A researcher wants to estimate the average farm size in a certain province. From a sample random of 40 farms, the
researcher obtains a sample mean farm size of 731 acres. Identify the parameter and statistic of the study.
A. The statistic is the average farm size in the province while the parameter is the mean farm size of 731 acres from the
sample of 40 farms.
B. The parameter is the average farm size in the province while the statistic is the mean farm size of 731 acres from the
sample of 40 farms.
C. The parameter is 731 acres in the province while the statistic is the mean farm size of in the province.
D. The statistic is the sample random of 40 farms while the parameter is 731 acres in the province.

Summative Test No.2 Score:

______

For numbers 1-4 consider the given situation.

The father of a senior high school student is listing down the expenses he will incur when he sends his daughter to the university.
At the university where he wants his daughter to study, he hears that the average tuition fee is at least Php20,000 per semester.
He wants to do a test of hypothesis. Suppose from a simple random sample of 16 students, a sample mean of Php19,750 was
obtained. Further, the variable of interest, which is the tuition fee in the university, is said to be normally distributed with an
assumed population variance equal to Php160,000 and level of significance 𝛼=5% 0𝑟 0.05.
_____ 1 .Identify the level of significance.
A. 0.5% B. 5% C. 0.10 D. 0.5
_____ 2.What kind of test will be used in the situation above?
A. One-tailed test. B. Two-tailed test C. Three-tailed test D. No-tailed test
____3. What test statistic to be used?
A. zc = 𝑥−𝜇𝑠√𝑛 B. tc = 𝑥−𝜇𝑠√𝑛 C. tc = 𝜇−𝑥𝜎√𝑛 D. zc = 𝑥−𝜇𝜎√𝑛
_____ 4. What can you conclude, out from the decision made by the researcher .
A. Therefore, the father can say that the average tuition fee in the university where he wants his daughter to study is equal to Php20,000.
B. Therefore, the father can say that the average tuition fee in the university where he wants his daughter to study is at least Php20,000.
C. Therefore, the father can say that the average tuition fee in the university where he wants his daughter to study is at most Php20,000.
D. Therefore, the father can say that the average tuition fee in the university where he wants his daughter to study is at greater that Php20,000.
_____5. The university dean believes that majority of his students in a class (60%) will get high scores this semester.
In a random sample of 65 students, 43 got high scores. Based on the data, formulate the appropriate hypotheses.
A. Null Hypothesis: 𝐻0:𝑝=0.60 vs. Alternative Hypothesis: 𝐻𝑎:𝑝≥0.60
B. Null Hypothesis: 𝐻0:𝑝=0.60 vs. Alternative Hypothesis: 𝐻𝑎:𝑝≤0.60
C. Null Hypothesis: 𝐻0:𝑝=0.60 vs. Alternative Hypothesis: 𝐻𝑎:𝑝≠0.60
D. Null Hypothesis: 𝐻0:𝑝=0.60 vs. Alternative Hypothesis: 𝐻𝑎:𝑝>0.60
_____6. If the dean believes that on average students have a GPA of 72%. Being the data-driven researcher that you
are, you can’t simply agree with his opinion, so you start testing.
Give the exact pair of hypotheses.
A. The null hypothesis is: The population mean grade is at most 72%, and the alternative hypothesis is: The population mean grade is not 72%.
B. The null hypothesis is: The population mean grade is 72%, and the alternative hypothesis is: The population mean grade is at least 72%.
C. The null hypothesis is: The population mean grade is greater than 72%, and the alternative hypothesis is: The population mean grade is not 72%.
D. The null hypothesis is: The population mean grade is 72%, and the alternative hypothesis is: The population mean grade is not 72%.
_____ 7.The rejection region refers to the region where the value of the test statistic lies for which we will reject the null
hypothesis. This region is also called
A. Critical region C. Hypothesis testing region
B. Probability region D. Z – score region
_____ 8. For a z-test of proportions, which of the following is the rejection region for a two-tailed test?
A. z > zα or z > -zα C. z < zα or z > -zα
B. z < -zα/2 or z > zα/2 D. z > -zα/2 or z > zα/2
_____ 9.For a z-test of proportions, which of the following is the rejection region for a one-tailed test?
A. z > + zα or z < -zα C. z > zα or z > -zα
B. z < + zα or z > -zα D. z > -zα/2 or z > zα/2
_____ 10. If your statement asks “Is the average growth rate greater than 12cm a day?” What kind of test
you are going to use?
A. Three-tailed test. B. Two-tailed test C. One-tailed test D. No-tailed test
_____ 11. Given the following: n = 30; 𝜇=10,000; 𝑥̅=9,750 ; 𝜎2=200,000 , compute for the value of the test statistic.
A. 2.03 B. 2.30 C. 3.0 D. 3.06
_____ 12.If you wanted to be 95% confident that your results are significant, what alpha level would you choose?
A. 0.1% B. 0.5% C. 5% D. 10%
Summative Test No.3 Score:
______

_____ 1. In a two-tailed type of test, what symbol you are going to use in an alternative hypothesis?
A. > B. < C. = D. ≠
_____2. This helps to decide whether to accept or reject a formulated statement after evaluation of the
sample.
A. Hypothesis testing C. Use of any test statistic
B. Using significance level D. Avoiding type I and type II Error
_____3. The rejection region can be located on the following except.
A. On top of the normal curve
B. On both sides with the nonrejection region in the middle
C. On the left side of the nonrejection region
D. On the right side of the nonrejection region
_____4. The standardized test statistic for large sample hypothesis test concerning a single population
proportion is represented by this formula.
A. 𝑧=𝑝̂−𝑝0𝑝0(1−𝑝0)𝑛 B. 𝑧=𝑝̂−𝑝0√𝑝0(1−𝑝0)𝑛 C. 𝑧=𝑥̅−𝜇𝑠√𝑛 D. 𝑇=𝑥̅−𝜇𝑠√𝑛
_____5. A Senior High School in the Division of Negros Oriental reported that out of 5000 Academic
Track students, 1800 are in General Academic Strand (GAS), 2050 are in HUMSS, while all the rest
belong to STEM. What is the population proportion (p) for STEM?
A. 0.23 B. 0.36 C. 0.41 D. 0.77
_____6. A survey claims that 9 out of 10 doctors recommend aspirin for their patients with headaches. To test this claim, a
random sample of 100 doctors is obtained. Of these 100 doctors, 82 indicate that
they recommend aspirin. Is this claim accurate? Use alpha = 0.05. What pair of null and alternative
hypothesis that best fits in this survey?
A. 𝐻0:𝑝=0.90 𝑎𝑛𝑑 𝐻𝑎:𝑝 <0.90
B. 𝐻0:𝑝=0.90 𝑎𝑛𝑑 𝐻𝑎:𝑝 ≈0.90
C. 𝐻0:𝑝=0.90 𝑎𝑛𝑑 𝐻𝑎:𝑝
D. 𝐻0:𝑝=0.90 𝑎𝑛𝑑 𝐻𝑎:𝑝 >0.90
_____7. This refers to a chart showing several different types of relationships between two variables.
A. Bivariate data B. Scatter Plot C. Correlation Coefficient D. Regression Analysis
_____8. This statistical method is used to determine whether there exists a relationship or association between two
variables.
A. Bivariate data B. Scatter Plot C. Correlation Coeffficient D. Regression Analysis
_____9. Which of the following is not a bivariate data?
A. Study a group of college students to find out their height and their weight
B. Study a group of diabetic patients to find their weights
C. Study a group of college students to find out their average SAT score and their age
D. Study a group of college students to find out their average standardized admission test (SAT) scores
_____10. George was curious about the relationship between population density (in people per
square kilometer) and average rent for 111-bedroom apartments in different cities. He took a
sample of cities and made this scatterplot:
George describes this scatterplot: “There is a positive linear association between population density
and average rent.
There don't seem to be any obvious outliers.” What is missing in the description?
A. Form B. Direction C. Strength D. Outlier
_____11. Which among the figures below has shown a negative correlation between the
number of hours a student watches television and his or her social studies test scores.

_____12. The number of hours spent on math homework each week and the final exam grades for
twelve students in Mr. Dylan’s algebra class are plotted below.
Based on a line of best fit, which exam grade is the best prediction for a student who spends about
4 hours on math homework each week.
A. 62 B. 72 C. 82 D. 92

Summative Test No.4 Score: ______

______1. In regard to symbols used in research methods, which of the following represents the dependent variable?
A. X B. Y C. Z D. None of the above
______2. The following are the Pearson’s correlation coefficient except
A. The value of r lies between -1 and 1, inclusive.
B. The size of |𝑟| indicates the strength of the linear relationship between x and y.
C. The value of r lies between -2 and 2, inclusive.
D. The sign of r indicates the direction of the linear relationship between x and y.
______3. It is the test statistic that measures the statistical relationship, or association, between two continuous
variables and it is based on the method of covariance.
A. Pearson’s correlation coefficient C. Kendall rank correlation
B. Spearman correlation D. Point-Biserial correlation
______4. Which of the following represents a positive linear correlation in an illustration below?

_______5. Given the computed correlation coefficient r below between the number of hours(x) spent in studying by the
students and their respective scores (y), interpret the value of correlation coefficient r .
SSxy = 1761 – (1/6)(92)(110) = 74.33
SSxx = 1426 – (1/6)(92)2 = 15.33
SSyy = 2418 – (1/6)(110)2 = 401.33
r = 0.948
A. There is a weak (very low) relationship between the number of hours studied and student’s score.
B. There is a strong (very high) relationship between the number of hours studied and student’s score.
C. No relationship between the number of hours studied and student’s score.
D. None of the above
_______6. Identify the independent variable: A social scientist explores if there is a link between socioeconomic status and
the number of children a family has.
A. Socioeconomic status C. Social scientist
B. Number of children D. None of the above
_______7. It is a statistical method that attempts to determine the strength and character of the relationship
between one independent variable ( x) and the dependent variables (y).
A. Z -test B. T- test C. Correlation D. Regression
_______8. A variety of summary statistics were collected for a small sample (10) of bivariate data, where the dependent
variable was y and an independent variable was x. Compute the sample correlation coefficient given the following:
ΣX = 90 Σ (Y − Y)(X − X) = 466 Σ ( ) 2 X − X = 234
ΣY = 170 Σ ( ) 2 Y − Y = 1434 SSE = 505.98
n = 10
A. -0.8015 B. 0.8045 C. 0 D. 1
_______9. A medical researcher wonders if the amount of airline travel a person engages in impacts how likely they are to
catch influenza during flu season. Identify the dependent variable.
A. Influenza infections
B. Amount of airline travel
C. Medical researcher
D. Flu season
______10. A researcher reports that the correlation between two quantitative variables is r = 0.8. Which
of the following statements is correct?
A. The average value of y changes by 0.8 when x is increased by 1.
B. The average value of x changes by 0.8 when y is increased by 1.
C. The explanatory variable (x) explains 0.8 of the variation in the response variable (y).
D. The explanatory variable (x) explains 2 8. = 0.64 of the variation in the response variable (y).

______11. A scatter plot and regression line can be used for all of the following EXCEPT
A. to determine if any (x,y) pairs are outliers.
B. to predict y at a specific value of x.
C. to estimate the average y at a specific value of x.
D. to determine if a change in x causes a change in y.

______12. If the coefficient of determination is 0.975, then which of the following is true regarding the slope of the
regression line?
A. All we can tell is that it must be positive.
B. It must be 0.975
C. It must be 0.987
D. Cannot tell the sign or the value