Basic Statistics (BS) — Winter 2024

Define the following terms: 1) Class Midpoint 2) Experiment 3) Ogive 4) Frequency Polygon 5) Event 6) Correlation 7) Scatter Plot

Construct a stem-and-leaf plot for the data given in the following table: Cloth Lengths (Centimeters)

Define Data. Explain levels of Data Measurement in detail with suitable example.

Abag Icontains 4 white and 6 black balls while another Bag II contains 4 white and black balls. One ball is drawn at random from one of the bags, and it is found to be black. Find the probability that it was drawn from Bag I.

Discuss the measures of variability in detail with suitable example.

Afair coin is tossed 10 times, what are the probability of getting exactly 5 heads and at least five heads.

For some computers, the time period between charges of the battery is normally distributed with a mean of 50 hours and a standard deviation of 15 hours. Rohan has one of these computers and needs to know the probability that the time period will be between 50 and 70 hours.

Explain Marginal, Joint, Union and conditional probabilities with suitable example.

Let sample mean be the mean of a random sample of size 50 drawn from a population with mean 112 and standard deviation 40. Find the probability that sample mean assumes a value between 110 and 114 and also find the probability that sample mean assumes a value greater than 113.

If 10% of a population of parts is defective, what is the probability of randomly selecting 80 parts and finding that 12 or more parts are defective?

Suppose scores on exams in statistics are normally distributed with an unknown population mean and a population standard deviation of 3 points. Arandom sample of 36 scores is taken and gives a sample mean score of 68. Find a 90% confidence interval to estimate the population mean exam scores.

Discuss the Sampling techniques in detail.

Acompany claims that their product weighs 500 grams on average. Asample of 64 products has a mean weight of 498 grams. The population standard deviation is known to be 8 grams. At a 1% significance level, is there evidence to reject the company’s claim?

Calculate a t-test (only calculated value) for the following data of the number of times people prefer coffee or tea in five time intervals. Coffee 4 5 7 6 9 Tea 3 8 6 4

Sketch a scatter plot from the following data, and determine the equation of the regression line. X 6 10 2 4 6 7 0 1 8 5 Y 82 88 56 64 77 92 23 41 80 59 47

Write a note on: 1) Null Hypothesis & Alternative Hypothesis 2) Type – I & Type – II Error

Compute SSE, Sand r2 for the following data: e X 61 63 67 69 70 74 76 81 Y 4.280 4.080 4.420 4.170 4.480 4.300 4.820 4.700 X 86 91 95 97 Y 5.110 5.130 5.640 5.560