Search & Filtering
Suppose that the probability of a person having a headache is 0.01, that the probability of a person having a fever given that the person has a headache is 0.4, and that the probability of a person having a fever is 0.02. Find the probability that a person has a headache given that the person has a fever.
A die that is loaded so that the numbers 1 and 3 are equally likely to appear and 2, 4, 5, and 6 are equally likely to appear. However, 1 is three times as likely to appear as 2.
(a) One die is rolled. Assign probabilities to the outcomes that accurately model the likelihood of the various numbers to appear.
(b) One die is rolled. What is the probability of getting a 3?
(c) One die is rolled. What is the probability of getting a 1 or a 4?
(d) One die is rolled. What is the probability of getting an even number?
Four microprocessors are randomly selected from a lot of 100 microprocessors among which 10 are defective. Find the probability of obtaining no defective microprocessors.
There are 5 green 7 red balls. Two balls are selected one by one without replacement. Find the probability that first is green and second is red.
A coin is thrown 3 times. List out the sample space. What is the probability that at least one head is obtained?
1. Why would a one-sample t-test be used over a z-test?
a. when the population mean is not known
b. when the population variability is not known
c. when the test is using a 1% significance level instead of 5%
d. if there are outliers present in the data '
2.Explain why you would conduct a paired-samples t-test.
. One such theory hypothesizes that people should spontaneously follow a
24-hour cycle of sleeping and waking-even if they are not exposed to the usual pattern of
sunlight. To test this notion, 8 paid volunteers were placed in a room in which there was no light from the outside and no clocks or other indicators of time. After a month in the room, each individual developed a cycle. Their cycles at the end of the study were as follows: 25, 27, 25, 23, 24, 25, 26, 25. Using the .05 significance level, determine if these participants’ cycles are different from a 24-hour cycle.
SS = 10,
Sample mean = 25
1.what is the null hypothesis?
2.what is the research hypothesis?
3.What is the comparison mean?
4.what is the comparison distribution?
5.What is/are the cutoff(s)?
6.what is the t score for the sample score?
7.How is the denominator of a t-score different from the denominator of a z-score?
8.what is your conclusion for this hypothesis test?
a) Mzee Kobe Bank wished to establish the times in seconds that each ATM transaction takes. A sample of ATM users were observed and the time in seconds each spent at the ATM was as follows:
Time (seconds)
10-19
20-29
30-39
40-49
50-59
Number of customer
15
60
67
98
2
i. Calculate the coefficent of variation of the waiting time? ( 6 marks)
A manufacturer turns out a product item that is labeled either “defective” or “not defective.” In order to estimate the proportion defective, a random sample of 100 items is taken from production, and 10 are found to be defective. Following implementation of a quality improvement program, the experiment is conducted again. A new sample of 100 is taken, and this time only 6 are found to be defective. (a) Give a 95% confidence interval on p_{1}-p_{2},
p1
−p2
, where p_1
p1
is the population proportion defective before improvement and p_2
p2
is the proportion defective after improvement. (b) Is there information in the confidence interval found in (a) that would suggest that p_{1}>p_{2} ?
p1
>p2
? Explain.
Use the rule method to describe the sample space S consisting of all points in the first quadrant inside a circle of radius 3 with center at the origin.
