1. The producer of a fuel added substance guarantees that the utilization of this added substance expands gas

mileage. An arbitrary example of 6 vehicles was chosen, and these vehicles were driven for one

week without the gas added substance and afterward for multi week with the added substance. The

following table gives the mileage (in miles per gallon) for these vehicles with and without the

added substance:

Vehicle 12 3 4 5 6

Mileage Without Additive 24.6 28.3 18.9 23.7 15.4 29.5

Mileage With Additive 26.3 31.7 18.2 25.3 18.3 30.9

Asuming mileages are ordinarily circulated, would you be able to infer that the utilization of the fuel

added substance expands mileage at the 2.5% importance level?

2. A scientist wished to appraise the contrast between the extent of clients of two

shampoos who are happy with the prodcut. In an example of 400 clients of Shampoo A

taken by this analyst, 78 said they are satisifed. In another example of 500 clients of

Cleanser B taken by a similar analyst, 92 said they were fulfilled.

a) Construct a 90% certainty stretch for the genuine distinction between the two populace

extents.

b) Based on your answer in (a), what might be your reaction at "=0.1 to the case that

there is no distinction in consumer loyalty between the two shampoos?

3. A study as of late detailed that the mean public yearly consumption for inpatient and

outpatient administrations of all people more than 64 years old was $5,423 with a norm

deviation of $979. An arbitrary example of 352 people over age 64 living in Sudbury had an

normal cost of $5,516.

a) Can we reason that the mean inpatient and outpatient cost of all Sudbury

occupants over age 64 is higher than the public normal of $5,423? Utilize the .01

level of importance.

b) Calculate the P-an incentive for this test. Would your answer have changed on the off chance that you had utilized a

.05 degree of importance?

QUESTION 3 (20 The credit-card purchases (in Rands) made by a family during a vacation is presented in the grouped frequency distribution below. Purchases (Rands) Frequency 200 1). (b) Find the joint cumulative distribution function F (x. ) of the two random variables. Include all the regions . (c) Find Pur