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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_______

Short Answer

Expert verified

a.H0:2.5

b.Ha:>2.5

Step by step solution

01

Given Information

A first-time convicted burglar spends an average of2.5 years in prison. The goal is to see if the average amount of time spent in prison has grown.

02

Explanation part a

  • The null hypothesis is
  • H0: A first-time convicted burglar spends less than or equal to 2.5years in prison.
  • The Null Hypothesis (H0): It's a declaration that there's no difference between sample means or proportions, or between a sample mean or proportions and a population mean or proportion.
03

Step 3: Explanation part b

  • The alternative hypothesis is:
  • Ha: A first-time convicted burglar spends more than 2.5years in jail on average.
  • Here's an alternative theory: It is the population assertion that contradicts H0, and it is what we conclude when we reject H0.
04

Step 4: Conclusion

For the above data, the null and alternative hypotheses are provided by:

H0:2.5

Ha:>2.5

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Most popular questions from this chapter

A Nissan Motor Corporation advertisement read, 鈥淭he average man鈥檚 I.Q. is 107. The average brown trout鈥檚 I.Q.is4. So why can鈥檛 man catch brown trout?鈥 Suppose you believe that the brown trout鈥檚 mean I.Q. is greater than four. You catch 12 brown trout. A fish psychologist determines the I.Q.s as follows: 5;4;7;3;6;4;5;3;6;3;8;5. Conduct a hypothesis test of your belief.

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鈥揳pproximately 1,200 students鈥搒mall city demographic) to determine if the local high school鈥檚 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.

Some of the following statements refer to the null hypothesis, some to the alternate hypothesis. State the null hypothesis, H0, and the alternative hypothesis. Ha, in terms of the appropriate parameter (orp).

a. The mean number of years Americans work before retiring is 34.

b. At most 60% of Americans vote in presidential elections.

c. The mean starting salary for San Jose State University graduates is at least \(100,000 per year.

d. Twenty-nine percent of high school seniors get drunk each month.

e. Fewer than 5% of adults ride the bus to work in Los Angeles.

f. The mean number of cars a person owns in her lifetime is not more than ten.

g. About half of Americans prefer to live away from cities, given the choice.

h. Europeans have a mean paid vacation each year of six weeks.

i. The chance of developing breast cancer is under 11% for women.

j. Private universities' mean tuition cost is more than \)20,000 per year.

Assume the null hypothesis states that the mean is at most 12. Is this a left-tailed, right-tailed, or two-tailed test?

"Phillip鈥檚 Wish," by Suzanne Osorio

My nephew likes to play

Chasing the girls makes his day.

He asked his mother

If it is okay

To get his ear pierced.

She said, 鈥淣o way!鈥

To poke a hole through your ear,

Is not what I want for you, dear.

He argued his point quite well,

Says even my macho pal, Mel,

Has gotten this done.

It鈥檚 all just for fun.

C鈥檓on please, mom, please, what the hell.

Again Phillip complained to his mother,

Saying half his friends (including their brothers)

Are piercing their ears

And they have no fears

He wants to be like the others.

She said, 鈥淚 think it鈥檚 much less.

We must do a hypothesis test.

And if you are right,

I won鈥檛 put up a fight.

But, if not, then my case will rest.鈥

We proceeded to call fifty guys

To see whose prediction would fly.

Nineteen of the fifty

Said piercing was nifty

And earrings they鈥檇 occasionally buy.

Then there鈥檚 the other thirty-one,

Who said they鈥檇 never have this done.

So now this poem鈥檚 finished.

Will his hopes be diminished,

Or will my nephew have his fun?

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