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Chapter 9: Q. 56 (page 540)

A bathroom scale claims to be able to identify correctly any weight within a pound. You think that it cannot be that

accurate. What type of test would you use?

Short Answer

Expert verified

In this scenario, a two-tailed test is used.

Step by step solution

01

Step :1 Introduction 

A two-tailed test is a statistical process that determines if a sample is greater or smaller than a certain range of values by using a two-sided critical area of a distribution. It's used in statistical significance testing and null hypothesis testing.

02

Explanation

According to a bathroom scale, any weight within a pound can be correctly identified. We don't think it's that precise.

As a result, we can see that the alternative hypothesis contains a (≠)sign. As a result, we find that a two-tailed test is appropriate in this circumstance.

Diagrammatic representation of two tailed test:

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Most popular questions from this chapter

The National Institute of Mental Health published an article stating that in any one-year period, approximately 9.5percent of American adults suffer from depression or a depressive illness. Suppose that in a survey of 100 people in a certain town, seven of them suffered from depression or a depressive illness. Conduct a hypothesis test to determine if the true proportion of people in that town suffering from depression or a depressive illness is lower than the percent in the general adult American population.

a. Is this a test of one mean or proportion?

b. State the null and alternative hypotheses.

H0:

Ha:

c. Is this a right-tailed, left-tailed, or two-tailed test?

d. What symbol represents the random variable for this test?

e. In words, define the random variable for this test.

f. Calculate the following:

i.x=

ii.role="math" localid="1649760873126" n=

iii.p'=

g. Calculate role="math" localid="1649760901479" σx=Show the formula set-up.

h. State the distribution to use for the hypothesis test.

i. Find the p-value.

j. At a pre-conceived α=0.05, what is your:

i. Decision:

ii. Reason for the decision:

iii. Conclusion (write out in a complete sentence):

According to the Center for Disease Control website, in 2011 at least18%of high school students have smoked a cigarette. An Introduction to Statistics class in Davies County,KY conducted a hypothesis test at the local high school (a medium sized–approximately 1,200 students–small city demographic) to determine if the local high school’s percentage was lower. One hundred fifty students were chosen at random and surveyed. Of the150 students surveyed, 82have smoked. Use a significance level of 0.05 and using appropriate statistical evidence, conduct a hypothesis test and state the conclusions.

Suppose that a recent article stated that the mean time spent in jail by a first-time convicted burglar is 2.5years. A study was then done to see if the meantime has increased in the new century. A random sample of 26first-time convicted burglars in a recent year was picked. The mean length of time in jail from the survey was 3years with a standard deviation of 1.8years. Suppose that it is somehow known that the population standard deviation is 1.5. If you were conducting a hypothesis test to determine if the mean length of jail time has increased, what would the null and alternative hypotheses be? The distribution of the population is normal.

a.Ho_______
b.Ha_______

"The Craven," by Mark Salangsang

Once upon a morning dreary

In stats class I was weak and weary.

Pondering over last night’s homework

Whose answers were now on the board

This I did and nothing more.

While I nodded nearly napping

Suddenly, there came a tapping.

As someone gently rapping,

Rapping my head as I snore.

Quoth the teacher, “Sleep no more.”

“In every class you fall asleep,”

The teacher said, his voice was deep.

“So a tally I’ve begun to keep

Of every class you nap and snore.

The percentage being forty-four.”

“My dear teacher I must confess,

While sleeping is what I do best.

The percentage, I think, must be less,

A percentage less than forty-four.”

This I said and nothing more.

“We’ll see,” he said and walked away,

And fifty classes from that day

He counted till the month of May

The classes in which I napped and snored.

The number he found was twenty-four.

At a significance level of 0.05,

Please tell me am I still alive?

Or did my grade just take a dive

Plunging down beneath the floor?

Upon thee I hereby implore.

The student academic group on a college campus claims that freshman students study at least 2.5 hours per day, on average. One Introduction to Statistics class was skeptical. The class took a random sample of 30 freshman students and found a mean study time of 137 minutes with a standard deviation of 45 minutes. At α=0.01 level, is the student academic group’s claim correct?
See all solutions

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