Statistics and Probability Answers

An acne specialist has found that 60% of acne sufferers are helped by existing treatments. He decides to test a new treatment on a random sample of 40 acne patients. If 28 of these respond to this treatment, can he conclude that it is significantly better at the 0.05 level?

a school administrator claims that less than 50% of the students of the school are dissatisfied by community cafeteria service. test this claim by using sample data obtained from a survey o 500 students of the school where 54% indicated their dissatisfaction of the community cafeteria service. use a =0.05

Q2) Prove that 

2

𝑛Γ(𝑛+

1

2

)

√𝜋

= 1 ∙ 3 ∙ 5 ⋯ ⋯ ⋯ (2𝑛 −

co-efficients of correlation, and The two regression equations from the following informationN= 10, ∑X= 350, ∑Y= 310, ∑(X-35)2 = 162, ∑(Y-31)2 = 222, ∑(X-35)(Y-31)= 92

Find the area to the left of critical value = 2.500 when the sample size is 29. [Hint: One-tailed test]

In a hospital’s emergency for Covid 19 patients, the average number of patients arriving 

between 9:00 a.m to 6:00 p.m is 7 per day. Find the probability that, on a given day, the 

number of patients arriving at the emergency room will be exactly (R + 1).

In a study to analyse performance of Advanced Negotiation course in a 2020 CIPS examination series the following scores in percentage were compiled for a sample of 100 candidates.

42,51,52,53,61,62,63,64,71,72,81,46,53,54,55,63,64,65,66,73,74,82,48,57,58,59,67,68,69,77,78,87,43,54,56,64,65,66,67,74,75,84,47,52,53,54,62,63,64,65,72,73,82,45,56,57,58,66,67,68,69,76,77,86,44,55,56,57,65,66,67,75,76,85,49,50,51,52,60,61,62,70,71,51,52,53,61,62,63,71,72,58,59,57,68,69,67,78,79,80

a)     Arrange the data in equal classes of size 10 starting from 40 percent.

b)     Using an ogive for the data, find

i)                  The approximate percentage of the candidates who passed the examination if the pass mark was 62.5 percent.

The pass marks if 90 percent of the candidate passed examination

If n=25 and the sample standard deviation is 15, construct a 95% confidence interval for the true standard deviation. (Assume the population is approximately Normal).

The following observations were randomly sampled from a Normal distribution. Using this data, construct a 99% confidence interval for the mean and interpret the interval. 8.11 12.06 10.01 12.01 8.59 9.35 10.79 11.74 7.42 11.72 8.44 7.67 10.93 8.42 8.50

If a researcher wants to estimate the proportion of customers of a coffee shop that favor the new brand of coffee the shop is serving to within 0.08 with probability 0.95, how many customers should they survey if the true proportion is assumed to be approximately 0.75 from previous studies?