Assignment 3 Week 9 And Week 11 Student Full Name

Assignment 3 Week 9 Week 11student Full Name

State whether the following statements are True or False. ( 6 marks , 1 Mark Each ) 1. A type I error is the mistake of rejecting the null hypothesis when it is actually true. 2. The null hypothesis is rejected if the P-value 0.05. 3. Two samples are dependent if the sample values are matched pairs. 4. In case of hypothesis testing for a sample, the t statistic is used if is not known and sample size n is greater than 30. 5. A claim that two population proportions are equal, each of the two samples must satisfy the requirement that and . 6. The Student t distribution and the normal distribution are symmetric.

Multiple Choice Questions: (6 marks, 1 Mark Each) 1. Area of the rejection region depends on … a. Size of α b. Size of β c. Test-Statistic. d. Number of values 2. A randomly selected sample of 1000 college students was asked whether they had ever used the drug ecstasy. Sixteen percent (16% or 0.16) of the 1000 students surveyed said that they had. Which one of the following statements about the number 0.16 is correct? a. It’s a sample proportion. b. It’s a population proportion. c. It’s a margin of error. d. It’s a randomly chosen number. 3. A decision in a hypothesis test can be made by using a a. P-value b. Critical Value c. A and B d. None of the above 4. When carrying out a large sample test of H0: = 10 vs. Ha: > 10 by using a rejection point, we reject H0 at level of significance when the calculated test statistic is: a. Less than b. Less than - c. Greater than d. Greater than 5. Sample sizes n1 = 50, n2 = 50 and numbers x1 = 15, x2 = 5 of successes to find the pooled estimate a. 0.4 b. 0.2 c. 2.0 d. None of the above 6. Two teams of workers assemble automobile engines at a manufacturing plant in Michigan. A random sample of 145 assemblies from team 1 shows 130 acceptable assemblies. A similar random sample of 125 assemblies from team 2 shows 120 acceptable assemblies. The pooled proportion for acceptable assemblies is: a. b. c. d.

Answer the following Essay Type Questions: (18 marks, 3 Mark Each) 1. The Pew Research Center claims that more than 55% of American adults regularly watch a network news broadcast. You decide to test this claim and ask a random sample of 425 Americans whether they regularly watch a network news broadcast. Of the 425 Americans, 255 responded yes. At α = 0.05, is there enough evidence to support the claim? 2. The scores on an aptitude test required for entry into a certain job position have a mean of at most 500. If a random sample of 36 applicants have a mean of 546 and a standard deviation of 120, is there evidence that their mean score is different from the mean that is expected from all applicants? Use a 0.05 level of significance. 3. Suppose a researcher believes that college faculty vote at a lower rate than college students. She collects data from 200 college faculty and 200 college students using simple random sampling. If 120 of the faculty and 150 of the students voted in the 2016 Presidential election, is there enough evidence at the 5% level of significance to support the researcher’s claim? Use the following information to answer Questions 4 and 5. Given the following data of two independent samples of normally distributed populations. Test the claim that at the α=0.05 level of significance. 5. Construct a 95% confidence interval about . 6. Can a person control certain body functions if that person is trained in a program of biofeedback exercises? An experiment is conducted to show that blood pressure levels can be consciously reduced in people trained in this program. The blood pressure measurements (in millimeters of mercury) listed below represent readings before and after biofeedback training of six subjects: Before: 136.9; 201.4; 166.8; 150.0; 173.2; 169.3. After: 130.2; 180.7; 149.6; 153.2; 162.6; 160.1. Do the data provide enough evidence to indicate that the mean blood pressure level decreases after training? Use α = 0.05.

Paper For Above instruction

This assignment involves a comprehensive understanding and application of fundamental statistical concepts including hypothesis testing, confidence intervals, and data analysis to real-world scenarios. The core of this task is to critically evaluate statements and data to draw informed conclusions using appropriate statistical methods.

The true/false questions assess foundational knowledge about hypothesis errors, the nature of the null hypothesis, the dependent and independent samples, the usage of t-statistics, and the symmetry of distributions such as the Student t and normal distributions. These are essential for understanding the logic behind statistical inference and for correctly designing hypothesis tests.

The multiple choice questions (MCQs) explore understanding of the rejection regions, sample proportions, decision rules based on p-values or critical values, and the calculation of pooled estimates in proportions. For example, recognizing that the area of the rejection region depends on significance level (α) is crucial for setting up hypothesis tests correctly.

The essay questions require applying statistical testing methods to specific datasets and hypotheses. The first involves testing a claim about the proportion of Americans watching network news, requiring a one-proportion z-test. The second involves evaluating whether the sample mean significantly differs from a known population mean with a t-test, considering the sample standard deviation and size.

Further, the third scenario examines comparing voting rates between college faculty and students, essentially a difference in proportions hypothesis test. The subsequent question involves interpreting data from two independent samples to test a claim at a specific significance level, emphasizing understanding of t-tests for independent samples.

Confidence intervals are also to be constructed to estimate the difference between two population parameters, providing a range of values with a specified confidence level such as 95%. This helps in understanding the precision of the estimates derived from sample data.

Lastly, an experiment related to biofeedback training assesses whether there is statistically significant evidence that training reduces blood pressure. This involves executing a paired sample t-test comparing before and after measurements.

In conclusion, this assignment synthesizes theoretical knowledge with practical data analysis skills. Accurate application of hypothesis testing, confidence interval construction, and critical interpretation of data are essential for effective statistical analysis. Proper understanding of the assumptions, calculation procedures, and interpretation of results will ensure valid conclusions aligned with research questions.

References

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