Search & Filtering
1.Given X and n, find p and q. Show your calculation steps.
a. X = 28; n = 100
b. X = 45; n = 240
c. X = 120; n = 1000
d. X = 234; n = 1500
e. X = 318; n = 2300
2.Estimate the population proportions for each of the following data:
a. In a plant box consisting of 120 seedlings, 80 seedlings were treated with growth enhancer. Estimate p and q, where p is the proportion of seedlings with growth enhancer.
b. In a survey of 80 children, 48 like to watch horror films. Find p and q, where p is the proportion of children who like to watch horror films.
3.In a political rally, an opinion poll was conducted among the present voters whether they agree with the platform of the candidate. Two hundred and one (201) said they agree. If there were 500 individuals in the sample, what is p? What is q?
In each of the following situations, identify the scale(s) of measurement that is appropriate for each situation.
(i) A visiting school inspector asked a class teacher to rank the thirty students in her class on “level of discipline”, with 1 standing for the least disciplined student and 30 standing for the most disciplined student.
(ii) Identical twins living in different environments are being compared to find out the influence of the environment on their academic performance. A standard test on academic performance is giving to fifty (50) sets of identical twins and their performance graded over 100.
EV (5 marks)
AN (5 marks)
[Total: 25 Marks]
2
(iii) “Regular” students and students admitted under the distance learning programme into Accra Institute of Technology are administrated a questionnaire measuring “level of maturity” of the students, with scores on “level of maturity” ranging from 0 to 10.
1.The mean scores of a random sample of 17 students who took a special test is 83.5. If the standard deviation of the scores is 4.1, and the sample comes from an approximately normal population, find the point and the interval estimates of the population mean adopting a confidence level of 95%.
a. point estimate
b. interval estimate
2.The mean age of 20 youth volunteers in a community project is 17.5 years with a standard deviation of 2 years. if the sample comes from an approximately normal distribution, what are the point and the interval estimates of the population mean? Use 99% confidence level.
a. point estimate
b. interval estimate
3.The average weight of 25 chocolate bars selected from a normally distributed population is 200 g with a standard deviation of 10 g. Find the point and the interval estimates using 95% confidence level.
a. point estimate
b. interval estimate
4.Explain the difference between a point estimate and an interval estimate.
1.Draw a normal curve showing the 99% confidence interval
2.Appliace manufacturers are required to post a sticker on their products regarding the electricity economy of each appliance for sale. Explain how this sticker indicates estimation in general.
3.Compare and contrast the z-distribution and the t-distribution.
4.Using t-table, give the confidence coefficients for each of the following:
a. n = 12 with 95% confidence
b. n = 15 with 95% confidence
c. n = 21 with 99% confidence
d. n = 23 with 95% confidence
e. n = 25 with 99% confidence
5.Assuming that the samples come from normal distributions, find the margin of error E 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
6.Using the information in number 3, find the interval estimates of the population mean.
a.
b.
c.
d.
e.
In a National Achievement Test, suppose three test
booklets are tested at random. Let D represent the
defective test booklet and let N represent the
non-defective test booklet. Let X be the random
variable representing the number of non-defective
test booklets
A researcher performs three independent hypothesis tests each at the 5% significance level.
Determine the probability of observing at LEAST one Type I Error. (Round your final answer to the nearest hundredth of a percent)
Two sample of votes for two candidates A and B for a public officer are taken one from among the residents of rural areas the results are given in the adjoining table examine whether the nature of the area is related to voting preference in this election
Question 8
Researchers investigating characteristics of gifted children
collected data from schools in a large city on a random sample of
thirty-six children who were identified as gifted children soon after
they reached the age of four. The following histogram shows the
distribution of the ages (in months) at which these children first
counted to 10 successfully. Also provided are some sample statistics.
Suppose
you read online that children first count to 10 successfully when they
are 32 months old, on average. You perform a hypothesis test evaluating
whether the average age at which gifted children first count to 10 is
different than the general average of 32 months. What is the p-value of
the hypothesis test? Choose the closest answer.
1.Given the following: the sampled population is normally distributed , n = 58, X = 75, and σ = 10.
a. What is the 99% confidence interval for μ?
b. Are the assumptions met? Explain your answer.
2.The ages of random sample of 60 Grade 9 students were obtained to estimate the mean age of all Grade 9 students. X = 15.3 years and the population variance is 16 years.
a. What is the point estimate for μ?
b. What is the 95% confidence interval for μ?
c. What is the 99% confidence interval for μ?
d. What conclusions can you make based on each estimate?
- Which of these illustrates confidence interval?
a. 0.95
b. 99%
c. 50.0
d. 90 - 95
2.What is the effect of the level of confidence on the confidence interval?
3.What is the margin of error E?
4.Given the information that a sampled population is normally distributed with X = 36, σ = 3 and n = 20.
a. What is the 95% confidence interval for μ?
b. Are the assumptions met? Explain
