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3) A social worker reports that 30% of workers in a factory are below 15 years of age. Of the 120 employees surveyed, 38 said they were below 15 years old. Using ? = 0.05, interpret the p-value.
2) A politician claims that she will receive 60% of the votes in the upcoming election. Of a random sample of 200 voters, there were 100 who will surely vote for her. Test the politician’s assertion at the 0.05 level of significance.
If h (θ) = cos2θ, find h(0), h (1/4π), h(1/2π)
A school administrator claims that less than 50% of the students of the school are dissatisfied
by the community cafeteria service. Test this claim by using sample data obtained from a survey of
500 students of the school where 54% indicated their dissatisfaction of the community cafeteria
service. Use 𝐠= 0.05.
1) Complete the table.
n X p₀ z p-value
a) 120 21 5%
b) 138 32 7%
c) 200 45 10%
d) 392 102 18%
e) 612 236 20%
f) 100 40 8%
g) 248 51 10%
h) 312 100 12%
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
#339914 on Dec 2023