STAT

CSTS-SEU-KSA

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Statistics (STAT-101)

Assignment-3 (Weeks: 9-11)

1st Semester, 1439-1440 (2018-2019)

Due date: 17/11/2018 (Time: 10:30 PM)

Student’s Name
Student’s ID
Section/CRN
Location

Marking Scheme
Question	Score	Obtained Score
Q-1	3
Q-2	3
Q-3	3
Q-4	3
Q-5	3
Q-6	3
Total	18

Note: You are required to fill your full name, ID and CRN.

1. A research conducted by the University of Michigan claimed that there are more female drivers in the USA than male drivers. A researcher decides to test this claim on his state. In his simple random sample of 400 observations, he noticed that 214 of 400 were women. At α = 0.05, is there enough evidence to support the claim?

(Use the critical value method where the critical value )

2. A machine is supposed to produce metal rods with a length of 8.30 cm. The length fluctuations due to manufacturing process correspond to a Standard deviation of 0.6 cm. Based on a random sample of size n = 100, and using the P-value method, we want to test if the machine is well adjusted at α = 0.05. The average length measured on the sample is 8.47 cm. Given that .

Hint: ; .

3. The mean height of a simple random sample of 36 supermodels is 70.0 inches and the standard deviation is 2.3 inches. Use a 0.01 significance level to test the claim that supermodels have heights with a mean that is greater than the mean height of 64.8 inches for women in the general population.

Given that Critical value of for (single tail) and 35 d.f. is 2.438

Hint:

4. A sample of 360 college graduates was surveyed, 200 of them were men and 160 were women, and each was asked if they earn more or less than $50,000 per year. The following data was obtained:

			Total
Men	120	80	200
Women	60	100	160
Total	180	180	360

Test the claim that the proportion of men earning over $50k is more than the proportion of women earning over $50k for . Given that the critical value .

Hint: ;

5. Two medicines A and B against the headache are compared based on the time of absorption by the body:

For the sample of drug A,

For the sample of drug B,

At the 5% significance level, is there a difference in absorption time between the two drugs if populations’ standard deviations are not equal.

Given the critical value of t for 40 d.f. and 0.05 significance level (Two-tailed) is 2.021.

Hint: H0 : μ1 = μ2 ; H1 : μ1 ≠ μ2

6. The following Table consists of five actual low temperatures and the corresponding low temperatures that were predicted five days earlier. Use a 0.05 significance level to test the claim that there is a difference between the actual low temperatures and the low temperatures that were forecasted five days earlier.

Table : Actual and Forecast Temperature

Actual low	32	35	37	36	38
Low forecast 5 days earlier	36	35	35	33	34
Difference = actualpredicted	4	0	2	3	4

Given that the mean and standard deviation of using above table are ,

Critical value of t for (two tail) with 4 d.f. is .

Hint: H0: μd = 0 ; H1: μd ≠ 0