Math Answers

Find the following limit.:

Lim x →0 for 1-cos x²/x².sin x²

List down 5 of Random Sampling and 5 examplesof Non Random Sampling. Also, identify if what particular random sampling and non sampling techniques are being applied.

First Column

Random Sampling

1.

2.

3.

4.

5.

Second Column

Non Random Sampling

1.

2.

3.

4.

5.

d) A random sample of size 36 was taken from a population distributed as Nμ,3.92.The value of the sample x was 15.6. i. Find a 90% confidence interval for μ.                                 (5mks)

It is believed that value of μ is 17. Use your confidence interval to comment on this belief.(2mks)

1. Using the provided information below,

x=33.2 , x2=131.67,  y=30.78 , y2=116.52, xy=119.8 , and n=10

1. Find the sample correlation coefficient r                                                                 (4mks)
2. Find the co-efficient of determination                                                                    (2mks)

study was made of a sample of 25 records of patients seen at a chronic

disease hospital on an

outpatient basis. The mean number of outpatient visits per patient was 4.8,

and the sample standard

deviation was 2. Can it be concluded from these data that the population mean

is greater than four

visits per patient? Let the probability of committing a type I error be .05. What

assumptions are

necessary?

A study by Thienprasiddhi et al. (A-4) examined a sample of 16 subjects

with open-angle glaucoma

and unilateral hemifield defects. The ages (years) of the subjects were:

62 62 68 48 51 60 51 57

57 41 62 50 53 34 62 61

Can we conclude that the mean age of the population from which the sample

may be presumed to have been drawn is less than 60 years? Let alpha = 0.5

7.2.2 A study by Thienprasiddhi et al. (A-4) examined a sample of 16 subjects 

with open-angle glaucoma

and unilateral hemifield defects. The ages (years) of the subjects were:

62 62 68 48 51 60 51 57

57 41 62 50 53 34 62 61

Can we conclude that the mean age of the population from which the sample 

may be presumed to have been drawn is less than 60 years? Let alpha = 0.5

Conduct P-value method

The Mathematics Department in a certain university is conducting a study to determine how long it takes its graduates to find a job. A sample of 80 graduates was surveyed and it was found out that the average time it has taken a graduate to find a new job is 2.5 months, with a standard deviation of 2 months. Is there a sufficient evidence to conclude that the graduate of this department takes on the average more than two months to find a job? Use the 90% confidence level. 

Consider all sample siza 5 fro this population 2 5 6 8 10 12 13 compute the mean u and standard deviation ó of the population