Question

In: Statistics and Probability

Suppose the null hypothesis is: Barb’s scuba gear is not safe. What would the type I...

Suppose the null hypothesis is: Barb’s scuba gear is not safe. What would the type I and II errors be in this situation? Further, what would be an appropriate choice for the level of significance? Explain your choice.

Solutions

Expert Solution

For specifying hypothesis we usually need more information for example you said barb's scuba gear is not safe...hypothesis is not specified like this. It always be specified in the terms of some characterstic.

Let's say you measure safety of the gear by how much time it can support someone underwater or let's say out of 100 , 90 % of the time it satisfied some safety test.

But let's say you are defining hypothesis like that

NULL HYPOTHESIS:  Barb's scuba gear is not safe

Alternative should be : Barb's scuba gear is safe

Type 1 error - You reject null hypothesis when it is actually true. That means barb's scuba gear was not safe but you accepted that it is safe by doing this you have committed type -1 error.

Type 2 error- You accept null hypothesis when alternative is true. i.e barb's scuba was safe but you declare it to be unsafe.

Choice of level of significance

The significance level is the probability of rejecting the null hypothesis when it is true.Lower significance levels indicate that you require stronger evidence before you will reject the null hypothesis.

so we will set significance level 1% usual practice is to set 5%,Reducing the alpha level from 0.05 to 0.01 reduces the chance of a false positive (called a Type I error) . So as in this case getting a false positive can be life threatning for barb so we try to lower the probability of type 1 error.


Related Solutions

Suppose the null hypothesis is: Barb’s scuba gear is not safe. What would the type I...
Suppose the null hypothesis is: Barb’s scuba gear is not safe. What would the type I and II errors be in this situation? Further, what would be an appropriate choice for the level of significance? Explain your choice.
Question 5 (5 marks) Suppose the null hypothesis is: Barb’s scuba gear is not safe. What...
Question 5 Suppose the null hypothesis is: Barb’s scuba gear is not safe. What would the type I and II errors be in this situation? Further, what would be an appropriate choice for the level of significance? Explain your choice.
Briefly explain/definition the basic concept of: i. The null hypothesis and the alternative hypothesis; ii. Type...
Briefly explain/definition the basic concept of: i. The null hypothesis and the alternative hypothesis; ii. Type I error and Type II error; iii. Power function; iv. Likelihood Ratio test; and v. Neyman-Pearson lemma.
What is a null hypothesis? Wat is an alternative hypothesis? Then articulate a null hypothesis and...
What is a null hypothesis? Wat is an alternative hypothesis? Then articulate a null hypothesis and alternative hypothesis for a research study that pertains to you're area of specialization. What conclusions can be drawn from this study with a "statistically significant" result?
For the following scenarios write an appropriate null and alternative hypothesis and identify what type of...
For the following scenarios write an appropriate null and alternative hypothesis and identify what type of test statistic will be used. (Steps 1 & 3 of the six step hypothesis test.) a. A nationwide sample of influential Republicans and Democrats was asked as part of a comprehensive survey whether they favored lowering environmental standards so that high-sulfur coal could be burned in coal-fired plants. The results were: Republicans Democrats No. Sampled 1100 1400 No. in Favor 115 158 At the...
1.   If a researcher rejects a null hypothesis, what type of error might they be committing?...
1.   If a researcher rejects a null hypothesis, what type of error might they be committing? a.   Type I, alpha b.   Type II, beta c.   Type III, sigma d.   Type IV, gamma 2.   The normal curve: a.   Is asymmetrical and asymptoptic b.   Has a mean, median and mode equal to zero c.   Has a standard deviation of zero d.   Can only be used as a descriptive statistic 3.   The Central Limit Theorem: a.   Can only be applied to characteristics with...
A. what type of test should be used and why? B. Compose a null hypothesis to...
A. what type of test should be used and why? B. Compose a null hypothesis to accompany the test. Record both a generic version (through the use symbols) and an English version (using words) – for the generic version, it may be easier to insert an equation box into the word document and type via equation C. Compose an alternative hypothesis to accompany the test. Record both a generic version (through the use of symbols) and an English version (using...
What is a null hypothesis and what is an alternative hypothesis?  How do you choose the null...
What is a null hypothesis and what is an alternative hypothesis?  How do you choose the null hypothesis in general? Give an example What is type I error? What is type II error? What is the significance level? What is the power of the test? What is the p-value of a hypothesis test?. Please type the answer. I have difficulties understanding handwritten answers. Thanks  
What is meant by a “null” hypothesis? How do you test a null hypothesis? What are...
What is meant by a “null” hypothesis? How do you test a null hypothesis? What are alternate hypotheses?   What are p-values? Explain "significance level." This is for business statistics
The correct answers are highlighted. I would like an explanation for why some are null hypothesis...
The correct answers are highlighted. I would like an explanation for why some are null hypothesis and some are alternative. Thank you. 4 You are testing the hypothesis that the mean textbook expense per semester at IUPUI is at least $500. The null and alternative hypothesis statements for this test are: a H₀: μ ≤ 500 H₁: μ > 500 b H₀: μ ≥ 500 H₁: μ < 500 c H₀: μ < 500 H₁: μ ≥ 500 d H₀:...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT