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(a) State hypotheses for a significance test to determine whether first responders are arriving within 8 minutes of the call more often. Be sure to define the parameter of interest.

(b) Describe a Type I error and a Type II error in this setting and explain the consequences of each.

(c) Which is more serious in this setting: a Type I error or a Type II error? Justify your answer.

(d) If you sustain a life-threatening injury due to a vehicle accident, you want to receive medical treatment as quickly as possible. Which of the two significance tests鈥H0:=6.7versusHa:<6.7 or the one from part (a) of this exercise鈥攚ould you be

more interested in? Justify your answer.

Short Answer

Expert verified

a. H0:p=0.78for null hypothesis and H0:p>0.78for alternative hypothesis

b. Type I error - the training needs improvement and Type II error - training needs no improvement

c. Type I error is more serious in this setting

d. With the population proportion of0.78

Step by step solution

01

introduction

The null hypothesis is a general explanation that expresses that there is no relationship between two peculiarities viable or that there is no relationship between two gatherings. An alternative hypothesis is an explanation that portrays that there is a relationship between two selected variables in a review

02

explanation part (a)

Given,

population proportion is 78%or 0.78

Calculating the null and alternative hypotheses,

H0:p=0.78as per the null hypothesis and H0:p>0.78ass per the alternative hypothesis

Thus, the population proportion is equal to 0.78for null hypothesis and greater than 0.78 for the alternative hypothesis.

03

explanation part (b)

In Type I error population proportion is 0.78that the first responder showed up quite a while after the mishap, yet it demonstrates that it is more. The result is that the reaction time has improved and the preparation doesn't need to be improved, however actually the preparation needs to move along.

In Type II error, when the null hypothesis is valid then dismissal of null hypothesis also failed. The population proportion is greater than0.78for the responder that showed up 8minutes after the mishap. Subsequently, rather than the reaction time, training should be improving, yet in reality, the preparation should not be gotten to the next level.

04

explanation part (c)

In Type II error The training has improved yet in Type I error, the training is not improved however in reality preparing should be worked on in Type I error.

Hence, Type I error is more serious.

05

explanation part (d)

The one with the population proportion 0.78since the significance test population mean is not more than 6.7minutes.

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Most popular questions from this chapter

A Gallup Poll report on a national survey of 1028 teenagers revealed that 72% of teens said they seldom or never argue with their friends. Yvonne wonders whether this national result would be true in her large high school. So she surveys a

a random sample of 150 students at her school.

Explain why we aren't safe carrying out a one-sample z test for the population proportion p.

You toss a coin 10 times to test the hypothesis H0:p=0.5 that the coin is balanced.

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results based on the total sample of national adults, one can say with 95% confidence that the margin of (sampling) error is 魛伅3 percentage points.鈥16 Can we use this interval to conclude that the actual proportion of U.S. adults who would say they want to lose weight differs from 0.55? Justify your answer.

鈥淚 can鈥檛 get through my day without coffee鈥 is a common statement from many students. Assumed benefits include keeping students awake during lectures and making them more alert for exams and tests. Students in a statistics class designed an experiment to measure memory retention with and without drinking a cup of coffee one hour before a test. This experiment took place on two different days in the same week (Monday and Wednesday). Ten students were used. Each student received no coffee or one cup of coffee, one hour before the test on a particular day. The test consisted of a series of words flashed on a screen, after which the student had to write down as many of the words as possible. On the other day, each student received a different amount of coffee (none or one cup). (a) One of the researchers suggested that all the subjects in the experiment drink no coffee before Monday鈥檚 test and one cup of coffee before Wednesday鈥檚 test. Explain to the researcher why this is a bad idea and suggest a better method of deciding when each subject receives the two treatments.

(b) The data from the experiment are provided in the table below. Set up and carry out an appropriate test to determine whether there is convincing evidence that drinking coffee improves memory.

Strong chairs? A company that manufactures classroom chairs for high school students claims that the mean breaking strength of the chairs that they make is 300pounds. One of the chairs collapsed beneath a 220-pound student last week. You wonder whether the manufacturer is exaggerating the breaking strength of the chairs.

(a) State null and alternative hypotheses in words and symbols.

(b) Describe a Type I error and a Type II error in this situation, and give the consequences of each.

(c) Would you recommend a significance level of0.01,0.05, or 0.10for this test? Justify your choice.

(d) The power of this test to detect =294is 0.71. Explain what this means to someone who knows little statistics.

(e) Explain two ways that you could increase the power of the test from (d).

- If conditions are met, conduct a significance test about a population proportion.

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