Statistics and Probability Answers

A random sample of size n is drawn from a uniform population over (θ-1/3,θ+1/3),Obtain maximum likelihood estimator ofθ.

A researcher wishes to see whether the mean of the heart rates (in beats per minutes) of smokers are different from the means of heart rates of people who do not smoke. The two samples are selected and the data are shown below. Using alfa = 0.05, is there enough evidence to support the claim?

Smoker

Non-smoker

n

60

60

Mean

79

86

s

32

38

 If a sample of 25 canned goods is selected, what is the probability that the mean of the sample will be larger than 20 mg?

A multiple choice quiz has 400 questions, each question with five possible answers of which one is correct answer. What is the probability that a sheer guess yields exactly 80 correct answers using normal approximation.

Nemi Mehta is owning 50 Hectares of land near Junagadh. On his Farm, he cultivates

Giloy, which is a medicinal plant in Ayurveda. The below-given table shows the sales

of ‘Giloy Vati’ that his team is preparing as per one Ayurveda script (book), and the

amount they spend on the Advertisement of it. Nemi’s problem is to analyze the effect of Advertisement on sales. Firstly, He wants to

understand the presence of a linear relationship between the sales and ‘amount spent in

advertisement’. He also wants to run a correlation and regression to know whether he

should keep spending money on Advertisements or not. If sales figures are not affected

by advertisement, he should not spend money on it.

So, take the EXCEL output of the following and write the interpretation.

 Appropriate type of Graph which can exhibit the linear relation b/w variables.

 Karl Pearson’s Correlation Coefficient

 Regression Analysis

 Graph that shows predicted v/s actual sales figures.

A LED company claims that the average life of the LED light bulbs it

manufactures is 1, 500 hours with a standard deviation of 500 hours. If a random sample of 40 bulbs is chosen, what is the probability that the sample mean will be:

a. greater than 1, 400 hours?

b. less than 1, 400 hours?

The mean and standard deviation of the tax value of all vehicles registered in

metro manila are 𝜇 = 𝑃ℎ𝑝 450 000 and 𝜎 = 𝑃ℎ𝑝 10000. Suppose random samples of 100 are drawn from the population of vehicles. Calculate the following:

a. mean of the sampling distribution

b. variance of the sampling distribution

b. standard deviation of the sampling distribution

Consider all possible samples of size 2 that can be drawn with replacement

from the population consists of numbers 1,2, and 3. Find the following:

a. mean of the sampling distribution

b. variance of the sampling distribution

c. standard deviation of the sampling distribution

The null hypothesis regarding a contingency table with 6 rows and 4 columns should be rejected (at 95% confidence) if the test statistic is greater than

Which one of the following probability distributions is used for determining whether or not a population has a Poisson probability distribution?