# 8.5 Additional information and full hypothesis test examples --  (Page 4/51)

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## Try it

A teacher believes that 85% of students in the class will want to go on a field trip to the local zoo. She performs a hypothesis test to determine if the percentage is the same or different from 85%. The teacher samples 50 students and 39 reply that they would want to go to the zoo. For the hypothesis test, use a 1% level of significance.

First, determine what type of test this is, set up the hypothesis test, find the p -value, sketch the graph, and state your conclusion.

Since the problem is about percentages, this is a test of single population proportions.

H 0 : p = 0.85

H a : p ≠ 0.85

p = 0.7554

Because p > α , we fail to reject the null hypothesis. There is not sufficient evidence to suggest that the proportion of students that want to go to the zoo is not 85%.

Suppose a consumer group suspects that the proportion of households that have three cell phones is 30%. A cell phone company has reason to believe that the proportion is not 30%. Before they start a big advertising campaign, they conduct a hypothesis test. Their marketing people survey 150 households with the result that 43 of the households have three cell phones.

Set up the Hypothesis Test:

H 0 : p = 0.30 H a : p ≠ 0.30

Determine the distribution needed:

The random variable is P′ = proportion of households that have three cell phones.

The distribution for the hypothesis test is $P\text{'}~N\left(0.30,\sqrt{\frac{\left(0.30\right)\cdot \left(0.70\right)}{150}}\right)$

a. The value that helps determine the p -value is p′ . Calculate p′ .

a. p′ = $\frac{x}{n}$ where x is the number of successes and n is the total number in the sample.

x = 43, n = 150

p′ = $\frac{\text{43}}{\text{150}}$

b. What is a success for this problem?

b. A success is having three cell phones in a household.

c. What is the level of significance?

c. The level of significance is the preset α . Since α is not given, assume that α = 0.05.

d. Draw the graph for this problem. Draw the horizontal axis. Label and shade appropriately.
Calculate the p -value.

d. p -value = 0.7216

e. Make a decision. _____________(Reject/Do not reject) H 0 because____________.

e. Assuming that α = 0.05, α < p -value. The decision is do not reject H 0 because there is not sufficient evidence to conclude that the proportion of households that have three cell phones is not 30%.

## Try it

Marketers believe that 92% of adults in the United States own a cell phone. A cell phone manufacturer believes that number is actually lower. 200 American adults are surveyed, of which, 174 report having cell phones. Use a 5% level of significance. State the null and alternative hypothesis, find the p -value, state your conclusion, and identify the Type I and Type II errors.

H 0 : p = 0.92

H a : p <0.92

p -value = 0.0046

Because p <0.05, we reject the null hypothesis. There is sufficient evidence to conclude that fewer than 92% of American adults own cell phones.

Type I Error: To conclude that fewer than 92% of American adults own cell phones when, in fact, 92% of American adults do own cell phones (reject the null hypothesis when the null hypothesis is true).

Type II Error: To conclude that 92% of American adults own cell phones when, in fact, fewer than 92% of American adults own cell phones (do not reject the null hypothesis when the null hypothesis is false).

Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
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what school?
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research.net
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sciencedirect big data base
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Introduction about quantum dots in nanotechnology
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What is lattice structure?
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or in general
Ebrahim
in general
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Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
how did you get the value of 2000N.What calculations are needed to arrive at it
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