# a social scientist believed that less than 30 percent of adults in the united states watch 15 or fewer hours of television per week. to test the belief, the scientist randomly selected 1,250 adults in the united states. the sample proportion of adults who watch 15 or fewer hours of television per week was 0.28, and the resulting hypothesis test had a p-value of 0.061. the computation of the p-value assumes which of the following is true?

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## A social scientist believed that less than 30 percent of adults in the United States watch 15 or

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A social scientist believed that less than 30 percent of adults in the United States watch 15 or fewer hours of television per week. To test the belief, the scientist randomly selected 1,250 adults in the United States. The sample proportion of adults who watch 15 or fewer hours of television per week was 0.28, and the resulting hypothesis test had a p-value of 0.061. The computation of the p- value assumes which of the following is true?

(A) The population proportion of adults who watch 15 or fewer hours of television per week is 0.28. Submit

(B) The population proportion of adults who watch 15 or fewer hours of television per week is 0.30.

(C) The population proportion of adults who watch 15 or fewer hours of television per week is less than 0.30.

(D) The population mean number of hours adults spend watching television per week is 15.

(E) The population mean number of hours adults spend watching television per week is less than 15.

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The **population proportion **of **adults **who watch **15** or fewer hours of **television** per **week **is **less **than** 0.3**0.

Given that,

A social **scientist **believed that **less** than **30 percent **of **adults **in the **United States** watch **15** or **fewer hours** of **television **per **week**.

The **scientist randomly **selected** 1,250 adults** in the** United States. **The **sample proportion **of **adults** who watch** 15** or **fewer** hours of **television **per week was **0.28, **

And the **resulting hypothesis **test had a** p-value** of** 0.061.**

We have to **determine,**

The **computation **of the** p- value** assumes which of the **following **is **true.**

**According**to the

**question**,

Let, The **proportion **of **adults **watching **television** **less **than or **equal** to** 15% **be =** x**

**Null Hypothesis**[

**H0**] :

**x**= 30% =

**0.30**

**Alternate Hypothesis**[

**H1**] :

**x < 30%**, or

**x**<

**0.30**

P **value **is **calculated** at** z value :**

Where **p' **= **0.28**, = **0.30**, = **0.70** ;

Then,

Assuming **10% level** of **significance**, **p = 0.10**

Therefore,** p **value** 0.061 < 0.10**, reject** H0** & accept** H1. **This implies that we conclude that 'x i.e. **proportion** of **adults** watching **television less **than or **equal **to **15% **< **30%** or** 0.30'**

Hence, The **population proportion **of **adults **who watch **15** or fewer hours of **television** per **week **is **less **than** 0.3**0.

To know more about **Sample proportion **click the link given below.

brainly.com/question/13846904

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### Answer

3.4/5 14 Ambitious 2.4K answers 8.6M people helped

**Answer:**

(C) The population proportion of adults who watch 15 or fewer hours of television per week is less than 0.30

**Step-by-step explanation:**

Let the proportion of adults watching television less than or equal to 15% be = x

Null Hypothesis [H0] : x = 30% = 0.30

Alternate Hypothesis [H1] : x < 30% , or x < 0.30

P value is calculated at z value : p' - [ √ { p0 (1- p0) } / n ] ;

where p' = 0.28, p0 = 0.30, p1 = 0.70 ; ∴ p ( z < -1.543) = 0.061

Assuming 10% level of significance, p = 0.10

As p value 0.061 < 0.10, we reject H0 & accept H1. This implies that we conclude that 'x ie proportion of adults watching television less than or equal to 15% < 30% or 0.30'

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## Solved Question 5 0 A social scientist believed that less

Answer to Solved Question 5 0 A social scientist believed that less

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**Question:** Question 5 0 A Social Scientist Believed That Less Than 30 Percent Of Adults In The United States Watch 15 Or Fewer Hours Of Television Per Week. To Test The Belief, The Scientist Randomly Selected 1,250 Adults In The United States. The Sample Proportion Of Adults Who Watch 15 Or Fewer Hours Of Television Per Week Was 0.28, And The Resulting Hypothesis Test

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Solution: We have to test a social scientist belief that less than 30% of adults in the U.S. watch 15 orfewer hours of television per week. T…

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Transcribed image text: Question 5 0 A social scientist believed that less than 30 percent of adults in the United States watch 15 or fewer hours of television per week. To test the belief, the scientist randomly selected 1,250 adults in the United States. The sample proportion of adults who watch 15 or fewer hours of television per week was 0.28, and the resulting hypothesis test had a p-value of 0.061. The computation of the p- value assumes which of the following is true? (A) The population proportion of adults who watch 15 or fewer hours of television per week is 0.28. Submit (B) The population proportion of adults who watch 15 or fewer hours of television per week is 0.30. The population proportion of adults who watch 15 or fewer hours of television per week is less than 0.30. D) The population mean number of hours adults spend watching television per week is 15. (E) The population mean number of hours adults spend watching television per week is less than 15.

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## CHAPTER 9 REVIEW AP CLASSROOM Flashcards

Start studying CHAPTER 9 REVIEW AP CLASSROOM. Learn vocabulary, terms, and more with flashcards, games, and other study tools.

## CHAPTER 9 REVIEW AP CLASSROOM

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The germination rate is the rate at which plants begin to grow after the seed is planted. A seed company claims that the germination rate for their seeds is 90 percent. Concerned that the germination rate is actually less than 90 percent, a botanist obtained a random sample of seeds, of which only 80 percent germinated. What are the correct hypotheses for a one-sample z-test for a population proportion p ?

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CORRECT ANSWER:C

H0:p=0.90Ha:p<0.90H0:p=0.90Ha:p<0.90

MY ANSWER: B H0:p=0.80Ha:p>0.80

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A one-sample z-test for a population proportion will be conducted using a simple random sample selected without replacement from a population. Which of the following is a check for independence

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CORRECT ANSWER:The population size is more than 10 times the sample size.

MY ANSWER: A

np0≥10np0≥10 and n(1−p0)≥10n(1−p0)≥10 for sample size nn and population proportion p0p0.

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### Terms in this set (26)

The germination rate is the rate at which plants begin to grow after the seed is planted. A seed company claims that the germination rate for their seeds is 90 percent. Concerned that the germination rate is actually less than 90 percent, a botanist obtained a random sample of seeds, of which only 80 percent germinated. What are the correct hypotheses for a one-sample z-test for a population proportion p ?

CORRECT ANSWER:C

H0:p=0.90Ha:p<0.90H0:p=0.90Ha:p<0.90

MY ANSWER: B H0:p=0.80Ha:p>0.80

A one-sample z-test for a population proportion will be conducted using a simple random sample selected without replacement from a population. Which of the following is a check for independence

CORRECT ANSWER:The population size is more than 10 times the sample size.

MY ANSWER: A

np0≥10np0≥10 and n(1−p0)≥10n(1−p0)≥10 for sample size nn and population proportion p0p0.

Consider a population with population proportion p, and a sample from the population with sample proportion pˆ. Which of the following describes the purpose of the one-sample z-test?

CORRECT ANSWER:D

To estimate the probability of observing a value as extreme as pˆp^ given p

MY ANSWER: To estimate the value of pp

Last year the mean cost μ for a one-bedroom rental in a certain city was $1,200 per month. Eli is looking for a one-bedroom apartment and is investigating whether the mean cost is less now than what it was last year. A random sample of apartments had a sample mean x¯ of $1,180 per month. Assuming all conditions for inference are met, Eli will conduct a hypothesis test as part of his investigation.

Which of the following is the correct set of hypotheses?

CORRECT ANSWER:B

H0:μ=1,200Ha:μ<1,200

MY ANSWER: B

H0:μ=1,200Ha:μ<1,200

A recent study reported the mean body mass index (BMI) for adults in the United States was 26.8. A researcher believes the mean BMI of marathon runners is less than 26.8. A random sample of 35 marathon runners had a mean BMI of 22.7 with a standard deviation of 3.1. The researcher will conduct a one-sample t-test for a population mean.

CORRECT ANSWER: A

Yes, all conditions have been met.

MY ANSWER: C

No, because marathon runners are not a representative sample of all adults in the United States.

To test the effectiveness of an exercise program in reducing high blood pressure, 15 participants had their blood pressures recorded before beginning the program and again after completing the program. The difference (after minus before) in blood pressure was recorded for each participant, and the sample mean difference x¯D was calculated. A hypothesis test will be conducted to investigate whether there is convincing statistical evidence for a reduction in blood pressure for all who complete the program.

Which of the following is the correct set of hypotheses?

CORRECT ANSWER: E

H0:μD=0Ha:μD<0MY ANSWER:B

H0:x¯D=0Ha:x¯D<0

A software company provides specialized resort reservation software that can be tailored to the needs of its customers. The company's 120 customers pay yearly subscription costs that can vary from customer to customer. The company knows that to be profitable, it needs each customer to be spending at least $23,000 per year, on average. The company selects a random sample of 33 customers and computes a mean of $27,871 and a standard deviation of $309.10. It performs a hypothesis test and computes a very small p-value. The software company concludes that the mean is greater than $23,000.

Was it appropriate for the software company to perform the hypothesis test and make the conclusion that was made?

CORRECT ANSWER:C

No, because the sample is more than 10 percent of the population, so one of the conditions for conducting a hypothesis test has not been met.

MY ANSWER: E

No, because the distribution of the sample data is skewed.

A six-week fitness program was designed to decrease the time it takes retired individuals to walk one mile. At the beginning of the program, 20 randomly selected retired individuals were invited to participate, and their times to walk a mile were recorded. After the six-week program, their times to walk a mile were again recorded. Most participants saw little to no improvement in their times to walk one mile; however, a few participants saw drastic improvements in their times to walk one mile. The program director would like to perform a hypothesis test to determine if the program reduces the mean time for retired individuals to walk a mile.

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