Statistics and Probability Answers

A car manufacturer claims that the average fuel consumption is 25 mpg (miles per gallon). To check the truth of this hypothesis, a study of 55 randomly selected cars. The results regarding the fuel consumption of the car are as follows:

30 27 22 25 24 25 24 15 35 35 33 52 49 10 27 18
20 23 24 25 30 24 24 24 18 20 25 27 24 32 29 27
24 27 26 25 24 28 33 30 13 13 21 28 37 35 32 33
29 31 28 28 25 29 31

(a). Estimate average fuel consumption for the entire population with a 95% confidence level.

(b). Conduct a hypothesis test to support or reject the claim of the producer, with a 95% confidence level.

A chip manufacturer tests the microprocessors produced from the production process. The company made a statement (claim) that only 4% of its microprocessor production was damaged. To test whether the claim is true, a study was conducted by taking a sample of 577 microprocessors, which found 37 of them were damaged. Can the statement (claim) be rejected or accepted with a 99% confidence level?

A Trade Union spokesman claimed that 75% of union members would support the strike if their basic demands were not met. The company spokesman believed that the actual percentage was smaller than the figure. He conducted the study, of which of the 125 samples, 87 trade union members which states will strike.

(a) Perform a hypothesis test with a 90% confidence level. Give analysis and conclusions

(b) Calculate the confidence interval for the percentage of members who say they will strike.

To find out / estimate the average value of the nominal shear strength of the steel beams in kN of all production, a test of 15 steel beam samples is carried out. The result is as follows:

580, 400, 428, 825, 850,875, 920, 550, 575, 750, 636, 360, 590, 735, 950

Estimate the average price (interval) of the steel beam population with a 99% confidence interval.

Let A and B be events in a sample space S. Prove that A and B are independent
if and only if P(A | B) = P(Ac
| B).

These reaction times (in tenths of a second) were recorded for group of subjects after each had been given a drug pain.



Drug A
4
7
6
3
4
3

Drug B
9
11
12
8
10
11

Drug C
8
6
7
6
5
7

Formulate the H0, and H1:
C.V. at alpha .01 level of significance
Compute the test value: ANOVA – F ratio
Decision
Interpretation

In a local referendum to legalize the sale of beer, voters were surveyed about their opinions on the referendum and their views on the moral issue of selling alcohol beverages. From the contingency table, test at 0.05 alpha whether their moral values are related to their opinion on the referendum:



Opinion on referendum



Drinking is :



For Against Undecided

OK

95

83

21

Tolerated

73

71

18

Immoral

12

46

8



Formulate the H0 and H1
C.V. at alpha 0.05 level of significance
Compute the test value: Chi-square X2
Decision
Interpretation

Correlation

The following are data for 12 individuals’ daily sodium intake and their systolic blood pressure readings. A research investigator is interested in learning how strong the association is between these variables and how well we can predict blood pressure from sodium intake. Test the association at alpha 0.01.

Person


1

2

3

4

5

6

7

8

9

10

11

12



Sodium (X)

6.8

7.0

6.9

7.2

7.3

7.0

7.0

7.5

7.3

7.1

6.5

6.4

BP (Y)

154

167

162

175

190

158

166

195

189

186

148

140





1. Formulate the H0 and H1
2. C. V. at alpha 0.01 level of significance
3. Compute the test value: Pearson r, then t-value
4. Decision
5. Interpretation

In a game of cards, a bridge is made up of 13 cards from a deck of 52 cards. What
is the probability that a bridge chosen at random contains
i) atmost 2 kings?
ii) 6 of one suit, 4 of another, and 3 of another?

A machine is a set to fill cereal boxes with the mean weight of 500 grams of cereal per box The standered deviation is known to be 25 grams. A random sample of 100 filled boxes is taken and the mean weight of cereal per box is computed as 504 grams. Is there reason to believe that machine is over filing the boxes use a=0.05