Math Answers

III – Find the approximate p-value given the following information:

1. A two-tailed test; computed t-value = 1.845; df = 10

2. A left-tailed test; computed t-value = 2.295; df = 21

3. A right-tailed test; computed t-value = 1.565; df = 27

4. A two-tailed test; computed t-value = 2.452; df = 12

Consider a population consist of 9, 5, 6, 12, and 15. Suppose that sample size of 2were drawn from this population (without replacement), describe the sampling distribution of the sample means

The average lot size of the houses in a small village is 55 square meters with a standard deviation of 10 square meters. Find the mean of the sampling distribution of the sample mean with a sample size of 50 houses if lot sizes are normally distributed.

df= 25 Percentile= 97.5th t(a,df) =

Water is flowing into a conical vessel 18 cm deep and 10 cm across the top at the rate of 4 cm3/min. The depth of the water is "h" cm. If the rate which the surface is rising is 0.1146 cm/min, find the value of "h"?

The Head of the Mathematics Department announced that the mean score of Grade 11

students in the first validating test in Mathematics was 65 and the standard deviation was 12.

One student who believed that the mean score was less than this, interviewed 50 randomly

selected students and obtained a mean score of 60. At 0.01 level of significance, test the

student's belief.

2. A simple random sample of 15 people from a certain population has a

mean age of 35 with a standard deviation of 20. Can we conclude that

the mean age of the population is younger than 35? Let alpha = .05.

Find the unit vector that is orthogonal to the vectors A=2i+j+k and B=-i+2j+k. Let the position of vectors of the vertices of triangle ∆ADC be OA=-2i+4j+k, OB=4i+j+k and OC=-7i+6k respectively. Use this information to answer

a)find the cosine of the angle between the side AB and AC

b)what is the the projection of the vector AC onto AB?

c)the area of the triangle ∆ABC can be calculated using?

d)find the area of the triangle ABC

A 9N force F1 and a 10N force F2 act in the same directions 2i+j-2k and 4i-3j respectively.

a) Find the resultant of the two forces

b)Find the total work done that the forces make the object move 2m along the vector s= i+j+k

c)find F1•F2

d)find F1 * F2

e)find the unit vector alone which the object will move to achieve maximum work done

f)what is the maximum work done that can be achieve if the tje forces displace the object by 1m

Read and analyze the following situations and supply the values of the following variables (if

there is any). On the third column, write known on the space provided if the situation gives

or can compute the value of the variance, otherwise write unknown. Identify also the formula

to be used to estimate the standard error of the mean by writing the symbols of, when the

population variance is known and sawhen the population variance is unknown,

Situation :

Given the population mean of 12, and a sample standard deviation of 3 in a sample size of 125

Given :

Answer :

Standard error formula :