Saudi Electronic University. Final STAT 101

Question 1

Saudi Electronic University. Final STAT 101. For a hypothesis test about a population mean, if the level of significance is 0.05 and the P-value is 0.20, then we fail to reject the null hypothesis.

• True
• False

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Question 2

The midpoint of the class interval 15-19 is 17.

• True
• False

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Question 3

P(X) = X/3 (Where X can be 0, 1, 2 or 3) determine a probability distribution.

• True
• False

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Question 4

Analysis of variance (ANOVA) is a method for testing the hypothesis that three or more population means are equal.

• True
• False

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Question 5

A quality control manager at a factory inspects a random sample of 400 light bulbs and finds that 8 of them are defective. The sample proportion of defective light bulbs is 0.02.

• True
• False

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Question 6

A box contains 3 black balls and 2 red balls. One ball is randomly selected. The probability of obtaining a black ball is 1/5.

• True
• False

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Question 7

The degree of freedom of t-test for independent samples (where σ₁ & σ₂ are unknown and are not assumed to be equal) with sample sizes n₁ = 43 and n₂ = 33 is equal to 42.

• True
• False

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Question 8

The mean of 4 values is 12. If 3 values are 8, 15 & 17, the missed value is 8.

• True
• False

Question 9

If a regression equation is ŷ = x + 1, then slope of this line is equal to 0.

• True
• False

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Question 10

In a goodness of fit test of n = 40 trials, if the no. of different categories or cells k = 5 and H₀: p₁ = p₂ = … = p₅ then expected frequency for each cell is 8.

• True
• False

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Question 11

For two tailed hypothesis test, the calculated test statistic z = 2.5, and the critical value of z = ±1.97. Then, the decision would be to:

• A. Reject H₀, since -1.97 < z < 1.97 Saudi Electronic University. Final STAT 101
• B. Reject H₀, since z > 1.97
• C. Cannot make a decision
• D. Fail to reject H₀, since z > 1.97

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Question 12

A random sample of size 49 from a normal population yields x̄ = 40 and σ = 7. The upper bound of a 95% confidence interval for the population mean μ (Z₀.₀₂₅ = 1.96) is:

• A. 41.04
• B. 38.04
• C. 42.00
• D. 41.96

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Question 13

With 0.05 significance level, H₀: μ ≥ 40, and the value of test statistics is z = 1.25, then the P-value is equal to (Given that P(z < 1.25) = 0.8944)

• A. -0.8944
• B. 0.8944
• C. 0.2112
• D. 0.1056

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Question 14

In a goodness of fit test of n = 100 trials, if the no. of different categories or cells k = 3 and H₀: p₁ = 0.1, p₂ = 0.3, p₃ = 0.6 then expected frequency for each cell is equal to

• A. 30, 10 and 60 respectively
• B. 10, 30 and 60 respectively
• C. 10, 60 and 30 respectively
• D. 60, 30 and 10 respectively

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Question 15

The number of observations falling within a class-interval is called

• A. Cumulative frequency
• B. Class midpoint
• C. Frequency
• D. Density

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Question 16

A fitted linear regression equation is y^​=10−2x. If x=5 and the corresponding observed value of y=2, then the residual at this observation is

• A 2
• B 0
• C -2
• D 4

Question 18

To test the hypothesis H0​:p1​=0.2;p2​=0.3;p3​=0.5 in a goodness of fit test, if the observed and expected frequencies are given as follows: O1​=14;O2​=36;O3​=50 E1​=20;E2​=30;E3​=50 The calculated chi square test statistic value is

• A 4.0
• B 2.0
• C 3.0
• D 1.0

Question 19

Test of hypothesis H₀: μ = 40 against Hₐ: μ < 40 leads to

• A. Sometimes Right Tail Test, sometimes Left Tail test
• B. Right Tail Test
• C. Two Tail Test
• D. Left Tail Test

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Question 20

Which of the following is not a correct way to state a null hypothesis?

• A. H₀: μ₁ – μ₂ = 0
• B. H₀: μ₁ – μ₂ > 0
• C. H₀: μ = 0
• D. H₀: μ₁ – μ₂ ≠ 0 Saudi Electronic University. Final STAT 101

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Question 21

A company claims that at least 65% of its customers are satisfied with their product. In a sample of 80 customers, 60 report being satisfied. To test the claim at a 0.05 significance level, the calculated test statistic for this hypothesis test is

• A. z = 1.216
• B. z = 3.316
• C. z = 1.716
• D. z = 1.875

Question 22

A researcher wishes to test for a difference in mean weights of a single species of fish caught by fishermen in different rivers in Yukon. The significance level for the test will be 0.05. Find the missing values in ANOVA table:

Source	SS	d.f.	MS	F
Treatment	?	3	4	2
Error	24	12	2
Total	36	15

• A 9
• B 12
• C 15
• D 18

Question 23

In ANOVA, if we are comparing k=5 groups of the same size n=5 and SS (Treatment) is given by 20, then MS (Treatment) is equal to

• A 5
• B 3
• C 4
• D 6

Question 24

A regression analysis for a study is performed. The Sum of Squares Error (SSE) is 40 and the Sum of Squares Total (SST) is 100. The coefficient of determination (r2) is: Saudi Electronic University. Final STAT 101

• A 0.4
• B 0.6
• C 2.5
• D 0.5

Question 25

A test of hypothesis H0​:ρ=0 against Ha​:ρ=0 is conducted to test the significance of the correlation coefficient. If the calculated t-statistic is 2.5 and the critical value is 2.1, the decision is:

• A Fail to reject H0​
• B Reject H0​
• C Accept H0​
• D None of the above

Question 26

Which of the following is true for the correlation coefficient (r)?

• A r can be greater than 1
• B r is always positive
• C −1≤r≤1
• D r has no relationship with the slope of the regression line

Question 27

For the following ANOVA table, calculate the F-statistic. Saudi Electronic University. Final exam stat 101

Source	SS	d.f.	MS	F
Treatment	20	4	5	?
Error	80	20	4

• A 1.25
• B 0.8
• C 5.0
• D 4.0

Question 28

In a study, the calculated value of a test statistic is 2.5 and the critical value is 1.96. The decision is:

• A Fail to reject H0​
• B Reject H0​
• C Accept H0​
• D None of the above

Question 29

If SS(Total)=100 and SS(Error)=60, then the SS(Treatment) is:

• A 160
• B 60
• C 40
• D 100

Question 30

The following data represents the number of defective items found in samples from four different shifts. Perform an ANOVA test at the 0.05 level of significance to test if there is a difference in the mean number of defects across shifts.

Shift 1	Shift 2	Shift 3	Shift 4
4	6	8	10
5	7	9	11

The calculated F-statistic is:

• A 4.0
• B 9.0
• C 2.0
• D 6.0

Question 31

In a study comparing the mean performance of three groups, the following results are obtained: SS(Total)=150 SS(Error)=90 The F statistic is 2.0. What is the SS(Treatment)?

• A 150
• B 90
• C 60
• D 20

Question 32

If the degrees of freedom for the treatment in an ANOVA test is 3 and the degrees of freedom for the error is 16, what is the total number of observations (N)? Saudi Electronic University. Final STAT 101

• A 19
• B 20
• C 18
• D 21

Question 33

A study is performed to investigate the relationship between the time spent studying and the test scores of students. The calculated correlation coefficient is r = 0.85. This indicates:

• A A weak negative relationship Saudi Electronic University. Final exam stat 101
• B A strong negative relationship
• C A weak positive relationship
• D A strong positive relationship

Question 34

For a goodness-of-fit test, if the observed frequencies are $O = \{10, 20, 30\} and expected frequencies are E = \{12, 18, 30\}, the chi-square statistic is:

• A 0.55
• B 0.556
• C 0.60
• D 0.45

Question 35

In a two-way ANOVA table, the degrees of freedom for the interaction effect are given by:

• A (r-1)(c-1)
• B r+c-1
• C n-1
• D k-1