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It is assumed that annual profit from farming depends on cultivated area.
a. Draw scatter plot of relationship between annual profit from farming and Cultivated Area, and comment.
b. State and interpret the correlation coefficient.
c. Test whether the coefficient of correlation obtained in (b) is significant at 5% level of significance. Show all five steps of Hypothesis testing.
d. Use simple linear regression to develop regression model. Estimate and interpret your model, intercept and slope. Properly present your model in terms of an equation.
during the college vacation, ahmed either eats rice with the probability of 0.6 or eats bread with the probability 0.4. ahned doesn't eat both on same day. .....fimd the probability that ahmed gains weight on any particular day
Employees of a large corporation are concerned about the declining quality of medical services provided by their group health insurance. A random sample of 100 office visits by employees of this corporation to primary care physicians during the year 2017 found that the doctors spent an average of 19 minutes with each patient. This year a random sample of 108 such visits showed that doctors spent an average of 15.5 minutes with each patient. Assume that the standard deviations for the two populations are 2.7 and 2.1 minutes, respectively. Using the 2.5% level of significance, can you conclude that the mean time spent by doctors with each patient is lower for this year than for 2017? To draw your conclusion, state the hypotheses and identify the claim, find the critical value(s), label the acceptance and rejection region, calculate the test value and summarize the results.
The length of time a full length movie runs from opening to credits is normally distributed with a mean of 1.9 hours and standard deviation of 0.3 hours. Calculate the following:
- A random movie is between 1.5 and 2.0 hours.
- A movie is longer than 2.4 hours.
- The length of movie that is shorter than 94% of the movies.
QUESTION 15
Assume that a weather forecast for tomorrow states that it rains in Johannesburg with probability
0.2, and it rains in Pretoria with probability 0.3. Assume further that we are told that if it does rain
in Pretoria, then it rains in Johannesburg with probability 0.8. Calculate the following:
(a) The probability that it rains in both Pretoria and Johannesburg. (4)
(b) The probability that it rains in at least one of the cities. (4)
(c) The probability that it does not rain in either city. (2)
(d) The probability that it rains in Pretoria, if it rains in Johannesburg. (4)
[14]
The mean weight of loads of rock is 47.0 tons with a standard deviation of 6.0 tons. If 16 loads are chosen at random for a weight check, find the probability that the mean weight of those loads is less than 46.2 tons. Assume that the variable is normally distributed.
Write the null hypothesis in words and in symbols.
1. A librarian of a school claims that all their Grade 9 students read an average of more than 10 books a month with a standard deviation of 2 books. A random sample of Grade 9 students read an average of 12 books a month with a standard deviation of 1 book.
3. A researcher thinks that if expectant mothers use vitamin pills, the birth weight of the babies will increase. The average birth weight of the population is 8.6 pounds.Write the null hypothesis in words and in symbols.
4. An engineer hypothesizes that the mean number of defects can be decreased in a manufacturing process of compact disks by using robots instead of humans for certain tasks. The mean number of defective disks per 1000 is 18.
Write the null hypothesis in words and in symbols.
3. A researcher thinks that if expectant mothers use vitamin pills, the birth weight of the babies will increase. The average birth weight of the population is 8.6 pounds.
Write the null hypothesis in words and in symbols.
1. A random sample of 200 students got a mean score of 62 with s-5 in a knowledge test in Mathematics. In the standardization of the test, -50 with o-10.
A biased die in favour of 4 where
p(4) =0.25 is thrown repeatedly until a 4 and a 5 have been obtained.
The random variable M denotes the number of throws required. For example, for the sequence of results
4, 3, 2, 3, 4, 4, 5, the value of M is 7. Calculate E(M) and Var(M)
#339914 on Dec 2023