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Find the dimensions of a right circular cone of minimum volume V that can be
circumscribed about a sphere of radius 8 inches.
show that p ↔ q and (p^q) v (¬p ^ ¬q) are logically equivalent.
A fast-food chain decided to carry out an experiment to assess the influence of advertising expenditure on sales. Different relative changes in advertising expenditure, compared to the previous year, were made in eight regions of the country, and resulting changes in sales levels were observed. The accompanying table shows the results
Increase in advertising expenditure (%) 0 4 14 10 9 8 6 1
Increase in sales (%) 2.4 7.2 10.3 9.1 10.2 4.1 7.6 3.5
a. Estimate the least-squares the linear regression of the increase in sales on increase in advertising expenditure
b. Find a 90% confidence interval for the slope of the population regression line
Use a Venn diagram to illustrate the subset of even integers in the set of all positive integers not exceeding 15.
Is the average amount spent on textbooks per semester by accounting majors significantly different from the average amount spent on text books per semester by management majors? Answer this question with a 90% confidence interval using the following data from random samples of students majoring in accounting or management. Discuss the assumptions
Accounting majors Management major
Mean $340 $285
Standard deviation 20 30
Sample size 40 50
Heights of the students in a class are given in the distribution below:
5' - 5'2" 10
5'2" - 5'4" 40
5'4" - 5'6" 25 .
Find:
1. Central Tendency
2. Dispersion
3. Skewness and kurtosis
A study is conducted in a company that employs 800 engineers. A random sample of 50 engineers reveals that the average sample age is 34.3 years. Historically, the population standard deviation of the age of the company’s engineers is approximately 8 years. Construct a 98% confidence interval to estimate the average age of all the engineers in this company
A card is drawn from a deck, then replaced, and a second card is drawn. Find the probability of selecting
- two pictures card
- a black card and an ace card
- a diamond and a king
- a lettered card and a number card
- a spade and a club
A clothing company produces men’s jeans. The jeans are made and sold with either a regular cut or a boot cut. In an effort to estimate the proportion of their men’s jeans market in Chilanga City that prefers boot-cut jeans, the analyst takes a random sample of 212 jeans sales from the company’s two Chilanga City retail outlets. Only 34 of the sales were for boot-cut jeans. Construct a 90% confidence interval to estimate the proportion of the population in Chilanga City who prefer boot-cut jeans.
A random sample of 10 students contains the following observations, in hours, for time spent studying in the week before final exams.
28 57 42 35 61 39 55 46 49 38
Assume that the population distribution is normal
(i) Find the sample mean and standard deviation
(ii) Test, at the 5% significance level, the null hypothesis that the population mean is 40 hours against the alternative that it is higher
#340153 on Dec 2023