Statistical Methods — Winter 2023

Define: Statistics. Explain in detail different scales of measurement.

Arandom sample of voters in Vadodara, Gujarat, is classified by age group, as shown by the following data. Calculate mean and standard deviation for the data. Age Group Frequency 18–under 24 17 24–under 30 22 30–under 36 26 36–under 42 35 42–under 48 33 48–under 54 30 54–under 60 32 60–under 66 21 66–under 72

Use the values in the matrix to solve the equations given. E F A 0.10 0.03 B 0.04 0.12 C 0.27 0.06 D 0.31 0.07 Find

P(A F)

P(E B)

P(B C)

P(E F)

Construct Box Plot for the data. OR1

In a manufacturing plant, machine Aproduces 10% of a certain product, machine Bproduces 40% of this product, and machine Cproduces 50% of this product. Five percent of machine Aproducts are defective, 12% of machine Bproducts are defective, and 8% of machine Cproducts are defective. The company inspector has just sampled a product from this plant and has found it to be defective. Determine the revised probabilities that the sampled product was produced by machine A, machine B, or machine C.

The Wall Street Journal reported some interesting statistics on the job market. One statistic is that 40% of all workers say they would change jobs for “slightly higher pay.” In addition, 88% of companies say that there is a shortage of qualified job candidates. Suppose 16 workers are randomly selected and asked if they would change jobs for “slightly higher pay.”

What is the probability that nine or more say yes?

What is the probability that three, four, five, or six say yes?

If 13 companies are contacted, what is the probability that exactly 10 say there is a shortage of qualified job candidates?

If 13 companies are contacted, what is the probability that all of the companies say there is a shortage of qualified job candidates?

Apen company averages 1.2 defective pen per carton produced (200 pens). The number of defects per carton is Poisson distributed.

Explain Type-Iand Type – II Errors in detail.

The Independent Insurance Agents of America conducted a survey of insurance consumers and discovered that 48% of them always reread their insurance policies, 29% sometimes do, 16% rarely do, and 7% never do. Suppose a large insurance company invests considerable time and money in rewriting policies so that they will be more attractive and easy to read and2 understand. After using the new policies for a year, company managers want to determine whether rewriting the policies significantly changed the proportion of policyholders who always reread their insurance policy. They contact 380 of the company’s insurance consumers who purchased a policy in the past year and ask them whether they always reread their insurance policies. 164 respond that they do. Use a 1% level of significance to test the hypothesis.

Explain different types of Sampling methods.

Arandom sample of size 70 is taken from a population that has a variance of 49. The sample mean is 90.4 What is the point estimate of ? Construct a 94% confidence interval for .

What is Hypothesis? Give the detail note on general process of testing of hypothesis.

The following data (in pounds), which were selected randomly from a normally distributed population of values, represent measurements of a machine part that is supposed to weigh, on average, 8.3 pounds. 8.1 8.4 8.3 8.2 8.5 8.6 8.4 8.3 8.4 8.2 8.8 8.2 8.2 8.3 8.1 8.3 8.4 8.5 8.5 8.7 Use these data and to test the hypothesis that the parts average 8.3 pounds.

Determine the value of correlation coefficient (r) for the following data. x 9 9 12 13 15 16 18 19 20 25 y 22 20 18 17 16 15 15 13 12 11

Determine the equation of the regression line for the following data and compute the residuals. X 15 8 19 12 Y 47 36 56 44 21