8. A drug and placebo were tested on 23 people each to study their effect on cholesterol. The mean cholesterol levels with the people on the new drug are 195 and SD of 35. The values for placebo sample are 245 and SD of 31. Using 5% level of significance, does the drug have effect on lowering the cholesterol.

The drug have effect on lowering the cholesterol.

Step-by-step explanation:

H₀ : μ₁ - μ₂ = 0

⇒ H₀ : μ₁ =  μ₂

H₁ : μ₁ - μ₂ < 0

⇒H₁ : μ₁ <  μ₂

Now,

given , n₁ = 23 , n₂ = 23

∴ Degree of freedom = v = n₁ + n₂ - 2

                                         = 23 + 23 - 2 = 44

⇒v = 44

Now,

Given, level of significance = 5% = 0.05

For the given significance level, critical time t = 1.68

As

Decision rule states that'if t < 1.68 , reject H₀

Now,

For Drug:

mean = m₁ = 195

SD = d₁ = 35

People = n₁ = 23

For placebo :

mean = m₂ = 245

SD = d₂ = 31

People = n₂ = 23

Now,

Variance =  = 1093

Standard Deviation, S = 33.06

Point estimate = m₁ - m₂ = 195 - 245 = -50

Standard deviation error = S×( ) = 9.75

Now,

Test statistics =

⇒ t < 6.13

⇒Reject H₀

⇒The drug have effect on lowering the cholesterol.

The answer is in the image 

SI=(P*R*T)/100

P=2000

R=1.5

T=6

SI=(2000*1.5*6)/100

=(2000*9)/100

=180

Neil will earn interest of 180

Cost of 7 gallons=$24.50

Cost of 1 gallon=24.50/7=3.5

Cost of 15 gallons=15*3.5=52.5

Cost of 15 gallons will be $52.5

The answer is in the image 

The answer is in the image 

The answer is in the image 

The answer is in the image 

The solution is given in the image below

Here,

tip=18%of $32

tip=(18/100)*32

=0.18*32

=$5.76

Total payment=32+5.76=$37.76