Purchase Solution

Type I and II errors and Confidence interval

Not what you're looking for?

Ask Custom Question

1. You have been asked to evaluate if a particular coin is fair or not. You have decided to use the following test:
Accept that the coin is fair if in 30 tosses the coin gives between 11 and 19 heads (inclusive); reject the hypothesis of fairness otherwise.

Compute the Type I error rate of this test. Interpret, in plain words, what the computed number would mean.

Compute the power (Type II error) of this test at p=.3, .49, .51, and .7. Interpret what the computed numbers mean. In addition, comment on any interesting patterns you found in these numbers. Then explain what is the cause of the patterns you discovered.

2. The time till first failure of a brand of HD plasma tvs is advertised to be more than 8 years. Suppose you sample 15 tvs of this type, keep track of them, and accept the advertised claim if the mean time to the first failure is larger than 8.5 years.
Plot the type I error probability and the power function of this particular test.

3. A t-statistic for testing H0: μ=3.5 is to be computed based on 20 observations with a mean of 4 and a standard deviation of 1.
Then, a 21st observation was collected and this new observation was 10. Recompute the t-statistic when all 21 observations are used.

Comment on what you find.

4. In 8 hospital rooms that are carpeted, and another 8 that are uncarpeted, bacteria per cubic ft. were counted, and the data are as follows:

Carpeted rooms: 11.8, 8.2, 7.1, 13, 10.8, 10.1, 14.6, 14
Uncarpeted rooms: 12.1, 8.3, 3.8, 7.2, 12, 11.1, 10.1, 13.7
Compute a nominal 90% confidence interval for the difference in mean bacterial count per cubic ft. in carpeted and uncarpeted hospital rooms. Discuss the pros and cons of each type of confidence interval for this particular application. Discuss what assumptions you would be concerned about and whether you can test them, if you have any doubts.

Purchase this Solution
Solution Summary

Step by step method for computing test statistic for hypothesis test is given in the answer.

Solution Preview

Please see the attached file.

You have been asked to evaluate if a particular coin is fair or not. You have decided to use the following test:
Accept that the coin is fair if in 30 tosses the coin gives between 11 and 19 heads (inclusive); reject the hypothesis of fairness otherwise.
Compute the Type I error rate of this test. Interpret, in plain words, what the computed number would mean.
The probability density function of binomial random variable with parameter n and p is given by the formula. .
Under H0. P =0.5

X P(X)
0 0.00000
1 0.00000
2 0.00000
3 0.00000
4 0.00003
5 0.00013
6 0.00055
7 0.00190
8 0.00545
9 0.01332
10 0.02798
11 0.05088
12 0.08055
13 0.11154
14 0.13544
15 0.14446
16 0.13544
17 0.11154
18 0.08055
19 0.05088
20 0.02798
21 0.01332
22 0.00545
23 0.00190
24 0.00055
25 0.00013
26 0.00003
27 0.00000
28 0.00000
29 0.00000
30 0.00000

Thus probability of rejecting H0 under p =0.5 = 1-0.9013 =0.0987. Thus there is a chance of 9.87% in concluding that the coin is not fair when in fact the coin is a fair one.
Compute the power (Type II error) of this test at p=.3, .49, .51, and .7. Interpret what the computed numbers mean. In addition, comment on any interesting patterns you found in these numbers. Then explain what is the cause of the patterns you discovered.
Type II error occur when concluding that the coin is fair when in fact the coin is biased. The probability for the accepting that for different values of p are given ...

Purchase this Solution
Free BrainMass Quizzes
Measures of Central Tendency

Tests knowledge of the three main measures of central tendency, including some simple calculation questions.

Measures of Central Tendency

This quiz evaluates the students understanding of the measures of central tendency seen in statistics. This quiz is specifically designed to incorporate the measures of central tendency as they relate to psychological research.

Terms and Definitions for Statistics

This quiz covers basic terms and definitions of statistics.

Know Your Statistical Concepts

Each question is a choice-summary multiple choice question that presents you with a statistical concept and then 4 numbered statements. You must decide which (if any) of the numbered statements is/are true as they relate to the statistical concept.

View More Free Quizzes
Related BrainMass Solutions

  • Point estimates and interval estimates

    22163 This solution finds point estimates for a mean and standard deviation as well as an interval estimate (confidence interval) for a population mean. Type I and Type II errors are discussed.

  • Hypothesis Testing And Central Limit Theorem

    540791 The solution gives detailed steps on determining type I and type II errors in a specific hypothesis testing and using confidence interval method to make the conclusion of the same test.

  • Random variable with exponential distribution

    This solution looks at hypothesis testing, showing how to find the probability of Type I and Type II errors occurring, the power function, and maximum likelihood estimations.

  • Bio Statistics

    311967 Biostatistics: Caffeine consumption; students who consume coffee; Type I and II errors #1. An investigator wants to estimate caffeine consumption in high school students.

  • Application of Confidence Intervals

    With your null who is bearing the risk of Type I and Type II errors? 2. What is the value of establishing confidence intervals in making business decisions? Give a specific example from your field of employment. 3.

  • Hypothesis Testing and Linear Regression Analysis

    Solution: The level of significance is the maximum probability of committing a type I error. The two errors associated with the level of significance are: Type I error and Type II error.

  • Confidence interal, standard error, Cohen's d, Type II

    377316 Confidence interal, standard error, Cohen's d, Type II 8.4. What are the five steps to create a confidence interval for a z distribution? 8.6.

  • Hypothesis Test Questions

    What does a Type I error mean in this situation? ii. What are the consequences of making a Type I error in this scenario? c. Type II error: i. What does a Type II error mean in this situation? ii.

  • Calculation of type I and type II error

    R1 = {x : x < 7 or x > 18} R2 = {x : x < 8} R3 = {x : x>17} ii. In the context of this problem situation, describe what type I and type II errors are. iii.

  • Correctly Identifying Type I and Type II Errors

    This solution is comprised of a detailed explanation of the Identification of Type I and Type II Errors. This solution mainly discussed the Type I and Type II Errors with clear examples.

View More Related Solutions