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Chapter 9: Q.75 (page 543)

From generation to generation, the mean age when smokers first start to smoke varies. However , the standard deviation pf that age remains constant of around 2.1years . A survey of 40smokers of this generation was done to see if the mean starting age is at least 19. the sample mean was 18.1 with a sample standard deviation of1.3do the data support the claim at the 5%level?

Short Answer

Expert verified

The true mean is significantly less than 19.

Step by step solution

01

Given Information

From the question itself we are given,

X=18.1represents the mean height for the sample .

s=1.3represents the sample standard deviation for the sample.

σ=2.1represents the population standard deviation for the sample .

n=40represents the sample size .

μ0=68represents the value that we want to test.

α=0.05represents the significance level for the hypothesis test.

twould represent the statistic ( variable of interest)

pvrepresents the p value for the test

02

Explanation

H0=μ≥19H0=μ<19

The statistic is given by:

z=X¯-μοσnz=18.1-192.140z=-2.71

Since it is a one sided test the p value would be ;

pv=P(z<-2.71)pv=0.0033

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Most popular questions from this chapter

You are testing that the mean speed of your cable Internet connection is more than three Megabits per second. State the null and alternative hypotheses.

A bottle of water is labeled as containing 16 fluid ounces of water. You believe it is less than that. What type of test would you use?

Over the past few decades, public health officials have examined the link between weight concerns and teen girls' smoking. Researchers surveyed a group of 273 randomly selected teen girls living in Massachusetts (between 12 and 15 years old). After four years the girls were surveyed again. Sixty-three said they smoked to stay thin. Is there good evidence that more than thirty percent of teen girls smoke to stay thin? The alternative hypothesis is:

a.p<0.30b.p≤0.30c.p≥0.30d.p>0.30

The mean age of De Anza College students in a previous term was 26.6 years old. An instructor thinks the mean age for online students is older than 26.6. She randomly surveys 56 online students and finds that the sample mean is 29.4 with a standard deviation of 2.1. Conduct a hypothesis test.

"Dalmatian Darnation," by Kathy Sparling

A greedy dog breeder named Spreckles

Bred puppies with numerous freckles

The Dalmatians he sought

Possessed spot upon spot

The more spots, he thought, the more shekels.

His competitors did not agree

That freckles would increase the fee.

They said, “Spots are quite nice

But they don't affect price;

One should breed for improved pedigree.”

The breeders decided to prove

This strategy was a wrong move.

Breeding only for spots

Would wreak havoc, they thought.

His theory they want to disprove.

They proposed a contest to Spreckles

Comparing dog prices to freckles.

In records they looked up

One hundred one pups:

Dalmatians that fetched the most shekels.

They asked Mr. Spreckles to name

An average spot count he'd claim

To bring in big bucks.

Said Spreckles, “Well, shucks,

It's for one hundred one that I aim.”

Said an amateur statistician

Who wanted to help with this mission.

“Twenty-one for the sample

Standard deviation's ample:

They examined one hundred and one

Dalmatians that fetched a good sum.

They counted each spot,

Mark, freckle and dot

And tallied up every one.

Instead of one hundred one spots

They averaged ninety six dots

Can they muzzle Spreckles’

Obsession with freckles

Based on all the dog data they've got?
See all solutions

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