Math Answers

y= log (1-2x)

1) If a hypothesis is conducted using 𝐠= 0.05, for which of the following p-values would the null hypothesis be rejected?

2) For each pair of ? and p-value, indicate whether the null hypothesis would be rejected.

3) In a test of H₀: µ = 80 against H₁: µ＜80, the sample data yielded the test statistic z = 1.63. What is

the p-value for the test?

4) In a test of H₀: µ = 80 against H₁: µ ≠ 80, a sample of observations had a mean and standard

deviation s = 4.1. What is the p-value for this test?

5) In a test of H₀: µ = 72 against H₁: µ ≠ 72, the sample data yielded the test statistic z = 1.63. Find the p-value for the test.

Drinking water has become an important concern among people. The quality of drinking water

must be monitored as often as possible during the day for possible contamination. Another variable of

concern is the pH level, which measures the alkalinity or the acidity of the water. A pH below 7.0 is

acidic while a pH above 7.0 is alkaline. A pH of 7.0 is neutral. A water-treatment plant has a target pH

of 8.0. Based on 16 random water samples, the mean and the standard deviation were found to be: X¯= 7.6 s = 0.4

Does the sample mean provide enough evidence that it differs significantly from the target

mean? In other words, does the sample come from a population whose mean is the same as the

target pH of ? Use , two-tailed test.

1.    Assuming that the samples come from normal distributions, find the margin of error  given the following:

a. n = 10 and X = 28 with s = 4.0, 90% confidence

b. n = 16 and X = 50 with s = 4.2, 95% confidence

c. n = 20 and X = 68.2 with s = 2.5, 90% confidence

d. n = 23 and X = 80.6 with s = 3.2, 95% confidence

e. n = 25 and X = 92.8 with s = 2.6, 99% confidence

2.    Using the information in number 2, find the interval estimates of the population mean.

A researcher used a developed problem solving test to randomly select 50 Grade 6 pupils. In

this sample, and . The mean and the standard deviation of the population used in

the standardization of the test were 75 and 15, respectively. Use the 95% confidence level

Given A =

{1, 2, 3, 4} and B = {x, y, z}. Let R be the following relation from A to B

R = {(1, y), (1, z), (3, y), (4, x), (4, z)}

a. Determine the matrix of the relation

b. Draw the arrow diagram of R

c. Find the inverse relation R^-1of R

d. Determine the domain

and range of R

A manufacturer of a flu vaccine is concerned about the quality of its flu serum. Batches of serum are processed by three different departments having rejection rates of 0.20, 0.08, and 0.21, respectively. The inspections by the three departments are sequential and independent.

(a) What is the probability that a batch of serum survives the first departmental inspection but is rejected by the second department?

(b) What is the probability that a batch of serum is rejected by the third department?

A manufacturer of a flu vaccine is concerned about the quality of its flu serum. Batches of serum are processed by three different departments having rejection rates of 0.20, 0.08, and 0.12, respectively. The inspections by the three departments are sequential and independent.

(a) What is the probability that a batch of serum survives the first two departmental inspection but is rejected by the third department?

(b) What is the probability that a batch of serum is rejected by the first department?