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A random sample of 100 likely voters in a small city produced 59 voters in favor of Candidate A. The observed value of the standardized test statistic for performing a test of H0:p=0.5H0:p=0.5versus Ha:p>0.5Ha:p>0.5

is which of the following?

a)z=0.59-0.50.59(0.41)100

b)z=0.59-0.50.5(0.5)100

c)z=0.5-0.590.59(0.41)100

d)z=0.5-0.590.5(0.5)100

e)z=0.59-0.5100

Short Answer

Expert verified

The test statistic is0.59-0.500.30(1-0.300100.

Step by step solution

01

Step 1:Given information

Number of trials (n)=100

Number of events(x)=59

Level of significance(α)=0.05

The null and alternative hypotheses are:

H0:p=0.5

Ha:p>0.5

02

Step 2:Explaination

The formula to compute the test statistic is:

z=p^-p0P01-p0n

Where,

p0 is the population proportion

p^ is the sample proportion

Now,

The sample proportion can be computed as:

Sample proportion(p^)=xn

=59100=0.59

Now, test statistic can be calculated as:

z=p^-p0p01-p0n

=0.59-0.500.50(1-0.50)100

Thus, the test statistic is0.59-0.500S5(1-0.000)100.

Hence, the correct option is (d).

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Most popular questions from this chapter

Members of the city council want to know if a majority of city residents supports a 1%increase in the sales tax to fund road repairs. To investigate, they survey a random sample of 300city residents and use the results to test the following hypotheses:

H0:p=0.50

Ha:p>0.50

where pis the proportion of all city residents who support a 1% increase in the sales tax to fund road repairs.

A Type I error in the context of this study occurs if the city council

a. finds convincing evidence that a majority of residents supports the tax increase, when in reality there isn’t convincing evidence that a majority supports the increase.

b. finds convincing evidence that a majority of residents supports the tax increase, when in reality at most 50%of city residents support the increase.

c. finds convincing evidence that a majority of residents supports the tax increase, when in reality more than 50%of city residents do support the increase.

d. does not find convincing evidence that a majority of residents supports the tax increase, when in reality more than 50%of city residents do support the increase.

Which of choices (a) through (d) is not a condition for performing a significance test about a population proportion p?

a. The data should come from a random sample from the population of interest.

b. Both np0and n(1-p0)should be at least 10.

c. If you are sampling without replacement from a finite population, then you should sample less than 10%of the population.

d. The population distribution should be approximately Normal unless the sample size is large.

e. All of the above are conditions for performing a significance test about a population proportion.

Walking to school Refer to Exercise 36.

a. Explain why the sample result gives some evidence for the alternative hypothesis.

b. Calculate the standardized test statistic and P-value.

c. What conclusion would you make?

According to the Bureau of Labor Statistics, the average age of American workers is 41.9years. The manager of a large technology company believes that the company’s employees tend to be younger, on average. So she takes a random sample of 12 employees and records their ages.

Here are the data:

27 38 32 24 30 47 42 38 27 43 37 33

a. State appropriate hypotheses for testing the manager’s belief. Be sure to define the parameter of interest.

b. State the conditions for performing a test of the hypotheses in (a), and determine whether each condition is met.

c. The P-value of the test is0.003. Interpret this value. What conclusion would you make?

Explaining confidence: Here is an explanation from a newspaper concerning one of its opinion polls. Explain what is wrong with the following statement.

For a poll of 1600 adults, the variation due to sampling error is no more than 3

percentage points either way. The error margin is said to be valid at the 95%

confidence level. This means that, if the same questions were repeated in 20 polls, the results of at least 19 surveys would be within 3 percentage points of the results of this survey.

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