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1) The sampling distribution of the statistic s12/s22 calculated from samples randomly selected from normally distributed populations, is A) a chi-squared distribution
1) The sampling distribution of the statistic s12/s22 calculated from samples randomly selected from normally distributed populations, is
A) a chi-squared distribution.
B) a normal distribution.
C) a t distribution.
D) an F distribution.
2) When the population standard deviation is known and the population values are normally distributed, which distribution is used in developing a test about the population mean?
A) Standard normal distribution.
B) Chi-squared distribution.
C) F distribution.
D) t distribution.
3) A sample of n observations was taken from a population. The appropriate chi-squared distribution used for statistical inference about the population variance has
A) n degrees of freedom.
B) n-1 degrees of freedom.
C) n-2 degrees of freedom.
D) n-k degrees of freedom.
4) Which of the following is not necessary to be known in order to compute the p-value?
A) Level of significance.
B) Numerical value of the test statistic.
C) Knowledge of whether the test is upper, lower, or two-tailed.
D) Sampling distribution of the test statistic.
5) Which of the following hypotheses can’t be tested with a chi-square test?
A) Intelligence (IQ score) and height are independently distributed in the human population.
B) 40% of American teenagers have a normal weight, 10% are underweight, 35% are overweight, and 15% are severely obese.
C) The logarithm of income is normally distributed within the population of the United Kingdom.
D) Women in Botswana give birth to their first child on average more than 1 year earlier than they get married.
6) In regression analysis, the explanatory variables are also called as
A) Dependent variables.
B) Independent variables.
C) Parameters.
D) Factors.
7) In regression analysis, the error term is a random variable with an expected value of
A) Any number.
B) One.
C) Any positive number.
D) Zero.
8) A regression model in which more than one explanatory variables are used to predict the dependent variable is called
A) an interactive model.
B) a multiple regression model.
C) an independent model.
D) a multi-dependent model.
9) In hypothesis testing, if the null hypothesis is rejected then
A) no conclusions can be drawn from the test.
B) the alternative hypothesis is accepted as true.
C) the data must have been accumulated incorrectly.
D) the sample provides sufficient evidence against the alternative hypothesis.
10) If a null hypothesis is rejected at the 5% significance level, then
A) it will always be rejected at the 10% significance level.
B) it will never be rejected at the 10% significance level.
C) it will never be accepted at the 1% significance level.
D) it will never be rejected at the 1% significance level.
Task 1 There is a factory in South Mexico producing canned tomato juice. Regarding the legislation the cans have to have a mean fill volume of at least 250 grams.
a. Formulate hypotheses that could be used to determine whether the mean fill volume satisfies the legal requirement.
b. We took a random sample of 20 cans from the production line of the factory (you can see the results in the G-H columns). Test your hypothesis using the p value approach. Interpret your results.
c. Test your hypothesis if the significance level=5%. What is your conclusion? Does the factory should adjust the settings of the production line?
Variable of interest y Filling volume
Null hypothesis H0
ONE-TAILED (LOWER TALE, CL) Alternative hypothesis H1
hypothesized value μ0
significance level α
sample size n
sample mean y_bar
SAMPLE standard deviation s
standard error SE(y_bar)
degree of freedom df
test statistics
type of test (LT/UT/2T)
p-value approach: p-value p
decision
Critical value approach: critical value
decision
consequence
|
Weights of the cans (grams) |
||
|
1 |
230 |
248 |
|
2 |
241 |
251 |
|
3 |
256 |
249 |
|
4 |
244 |
245 |
|
5 |
266 |
255 |
|
6 |
234 |
249 |
|
7 |
248 |
257 |
|
8 |
254 |
251 |
|
9 |
229 |
244 |
|
10 |
252 |
251 |
Task 2 The police has investigated that whether there is any association between use of safety belt and the outcome of the accidents. The data obtained are shown in the contingency table below. Use 1% significance level and test for the independence of habit using safety belt and the type of injuries. What is your conclusion? Points attained Points available
10
Observed frequencies (fij)
Safety belt used Safety belt not used Total
Minor injuries 512 229 741
Major injuries 99 125 224
Fatal injuries 13 22 35
Total 624 376 1000
Type of test
Null hypothesis H0
Alternative hypothesis H1
Number of rows p
Number of column q
Significance level α
Expected frequencies (eij)
Safety belt used Safety belt not used
Minor injuries
Major injuries
Fatal injuries
Total
χ2
Safety belt used Safety belt not used
Minor injuries
Major injuries
Fatal injuries
Total
Test statistic
Type of test (LT/UT/2T)
Degree of freedom DF
Critical value approach: Critical value
Decision
p-value approach: p-value p
Decision
Conclusion
Task 3 The following statistics is showing the price of flats in Budapest (in EUR) (PRICE) and 2 explanatory variables: area of the flat in nm (AREA) and age of the flat in years (AGE). PRICE AREA AGE Points attained Points available
71,000 34 11 1 10
a. Develop an estimated regression equation with (AREA) as the independent variable. Determine b0 and b1. Determine the estimated equation. 1,00,000 54 22 2
b. Develop an estimated regression equation with both explanatory variables (AREA and AGE). Determine b0, b1, b2. Determine the estimated equation. 2,95,000 120 2 3
c. Interpret the coefficient of the area in the two different models and explain the difference. 62,000 38 22 4
d. Compute R2 and adjusted R2. Which model is the better? Why? 1,95,000 86 4 5
e. What is the estimated price for a 68 m2 , 10 years old flat by both models? 1,11,000 96 25 6
4,88,000 200 3 7
a. b0= b1= 3,24,000 133 4 8
Equation 1,14,000 50 13 9
b. b0= b1= b2= 88,000 46 55 10
Equation 1,88,000 88 6 11
c. Interpretation: 2,00,000 77 10 12
93,000 44 18 13
1,60,000 92 12 14
d. Simple regression model Multiple regression model 1,59,000 77 1 15
R-square = R-square =
Adj.R-square = Adj.R-square =
Model selection, explanation
e. Projection with the simple regression model Projection with the multiple regression model
Estimated price = Estimated price =
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