Statistical Methods — Winter 2019

Define the following terms. 1) Correlation 2) Independent Events 3) Confidence Intervals 4) Null Hypothesis

For the following data obtain five number summary and also draw box plot. 22,25,23,28,32,19,28,29,35,38,36,39,42,15,23,24,26,27,28

Write different levels of Data Measurements in brief.

Obtain correlation coefficient for the following data: X 12 13 14 15 16 17 18 19 20 21 Y 25 24 26 28 20 29 24 26 28 30

In a study of job satisfaction, a series of tests was administered to 50 subjects. The following data were obtained: higher scores represent greater dissatisfaction. Construct a stem-and-leaf display for the data.

For events Aand B , P (A’ ∩ B) = 0.1, P (A∩B’) = 0.4 and P (A’ U B’) = 0.6 Find the (1) P (A) (2) P (B) (3) P (A U B) (4) P (A’ U B)

Define the normal distribution. Marks of large number of students are distribution normally with mean 55 and standard Deviation 13. If a student is selected at random what is the probability that his marks will be Between (1) 43 and 67 (2) 35 and 75 (3) More then 60

Phone calls arrive at the rate of 36 per hour at the reservation desk for Regional airways. (1) Compute the probability of receiving three calls in a three minute interval of time. (2) Compute the probability of receiving exactly 5 calls in ten minutes. (3) If no calls are being processed, what is the probability that the agent can take two minutes for personal time without being interrupted by a call?

(1) Apsychologist determined that the number of sessions required obtaining the trust of patient is either 1, 2 or 3. Let Xbe a random variable indicating the number of sessions required to gain patient’s trust. For given probability1 function f(x) = x/6) where x=1, 2 or 3; compute expected value and variance of X. (2) For two mutually events Aand Bhaving P(A)=0.3 and P(B)=0.4, compute P(AUB) and P(A|B).

Apopulation has a mean of 50 and a standard deviation of 10. If a random sample of 64 is taken, what is the probability that the sample mean is each of the following? a. Greater than 52 b. Less than 51 c. Less than 47 d. Between 48.5 and 52.4 e. Between 50.6 and 51.3

Arandom sample of size 39 is taken from a population of 200 members. The sample mean is 66 and the population standard deviation is 11. Construct a 95% confidence interval to estimate the population mean. What is the point estimate of the population mean?

Write brief note for different types of Sampling Methods.

Suppose the following data are selected randomly from a population of normally distributed values. 40, 51, 43, 48, 44, 57, 54, 39, 42, 48, 45, 39, 43 Construct a 95% confidence interval to estimate the population mean.

According to a study several years ago by the Personal Communications Industry Association, the average wireless phone user earns $62,600 per year. Suppose a researcher believes that the average annual earnings of a wireless phone user are lower now, and he sets up a study in an attempt to prove his theory. He randomly samples 18 wireless phone users and finds out that the average annual salary for this sample is $58,974, with a population standard deviation of $7810. Use  = .01 to test the researcher’s theory. Assume wages in this industry are normally distributed.

For the Following Data X 1 1 1 1 1 Y 2 3 3 4 Calculate (1)Develop a Scatter diagram for this data. (2)Compute the estimated regression equation. (3)Compute SSE, SST AND SSR. (4)Compute the coefficient of determination r 2 and comment on the goodness of fit.

Explain type Iand type II errors.

Develop a one-way ANOVA on the following data. Determine the observed Fvalue. Compare it to the critical Fvalue and decide whether to reject the null hypothesis. Use a 1% level of significance.