Statistics and Probability Answers

1 Information about data
You want to investigate the conditions of the apartments in city A. You selected simple
random sample of 50 apartments and got these data:
1. year: age of the building where an apartment is (in years).
2. area: the area of the apartment (in square meters).
3. price: price of the apartment (in euro).
2 Tasks for laboratory work 2
1. Task 1. Calculate main characteristics for each variable;
2. Task 2. Calculate the 95% confidence interval for the average of price;
3. Task 3. Verify hypothesis, that the average year is equal to 15.
4. Task 4. Verify hypothesis, that the average area is more than 45.
5. Task 5. Group your data by the year in these groups: 0-5; 6-10; 11-15; 16-20; 21-25;
26-30 and calculate all frequencies. Draw empirical density function.
6. Task 6. Group your data by the area in these groups: 30-39; 40-49; 50-59; 60-69; 70-79;
80-89; 90-99 and calculate all frequencies. Draw empirical density fun

The mean diameter of a population of newly-settled periwinkles is 8.5 cm with a
standard deviation of 0.10 cm. What is the probability of selecting a random sample of
100 winkles that has a mean diameter greater than 8.52 cm?

Johnson (1966) measured bills of dusky flycatchers and found that bill lengths of the
males had a mean of 8.15 ± 0.021 mm (mean ± SE) and a coefficient of variation of
4.67 %. On the basis of this information, infer how many specimens must have been
used in the sample.

Describe a real life example in your daily life through which you can set a hypothesis for single mean test. Explain thoroughly and solve the problem by choosing a suitable test statistic.

A bag contains 3 black balls.Paul picks a ball at random from the bag and without replaces it back in the bag.He mixes the balls in the bag and then picks another ball at random from the bag

(a) one of each colour

Maria’s phone bills were $95, $67, $43, and $115. What was the mean, or average, of her phone bills?
$55
$72
$80
$105

Q3. Two companies manufacture a rubber material intended for use in an automotive application. The part will be subjected to abrasive wear in the field application, so we decide to compare the material produced by each company are tested in an abrasion test, and the amount of wear after 1000 cycles is observed. For company 1, the sample mean and standard deviation of wear are x ̅1 = 20 milligrams/1000 cycles and s1 = 2 milligrams/1000 cycles, while for company 2 we obtain x ̅2 = 15 milligrams/1000 cycles and s2 = 8 milligrams/1000 cycles.
(a) Do the data support the claim that the two companies produce material with different mean wear? Use  = 0.05, and assume each population is normally distributed but that their variances are not equal.
(b) What is P-value for this test?
(c) Do the data support a claim that the material from company 1 has higher mean wear than the material from company 2? Use the same assumptions as in part (a).

The average rate of emission radioactive particles from a source was measured over a long period, and found to be 10 particles per unit time. After an experimental treatment had been applied to the source, a further sample was examined and emitted 17 particles in unit time. Test at 5% the null hypothesis that the rate of emissions is unchanged.

Two machines are used for filling plastic bottles with a net volume of 16.0 ounces. The fill volume can be assumed normal, with standard deviation 1 = 0.020 and 2 = 0.025 ounces. A member of the quality engineering staff suspects that both machine fill to the same mean net volume, whether or not this volume is 16.0 ounces. A random sample of 10 bottles is taken from the output of each machine.
Machine 1 Machine 2
16.03 16.01 16.02 16.03
16.04 15.96 15.97 16.04
16.05 15.98 15.96 16.02
16.05 16.02 16.01 16.01
16.02 15.99 15.99 16.00
(a) Do you think the engineer is correct? Use  = 0.05.
(b) What is the P-value for this test?
(c) What is the power of the test in part (a) for a true difference in mean of 0.04?

A University of Zululand student graduates with a Bachelor of Science degree in Agriculture (Agronomy) by passing 20 modules in total. The marks obtained for each module (in percentage form) are given below: 71 52 81 66 77 96 83 77 65 59 82 97 72 91 50 63 53 74 77 88 1.1 Group the data into a frequency distribution with the lowest class lower limit of 50 percent and a class width of 10 percent. (2 Marks) 1.2 Using the raw data determine the range. (2 Marks) 1.3 Determine the mean and mode from the raw data. (2 Marks) 1.4 Construct an OGIVE curve corresponding to the data. (4 Marks)