Question 1

Which of the following is NOT a requirement for using the normal approximation to the binomial distribution when testing a claim about a proportion?

Accepted Answer

The sample size $$n$$ must be greater than 30.

Question 2

Suppose you want to test the claim that the proportion of defective items produced by a factory is less than 5%. You collect a simple random sample of 200 items and find 6 defective items. What is the value of the sample proportion $$\hat{p}$$?

Accepted Answer

$$\hat{p} = \dfrac{6}{200} = 0.03$$

Question 3

What is the formula for the test statistic $$z$$ when testing a claim about a population proportion?

Accepted Answer

$$z = \dfrac{\hat{p} - p}{\sqrt{\dfrac{p(1-p)}{n}}}$$

Question 4

A survey of 1000 adults finds that 29% feel comfortable in a self-driving car. Test the claim that more than 1/4 of adults feel comfortable in a self-driving car. What are the null and alternative hypotheses?

Accepted Answer

$$H_0$$: p = 0.25$$; H_1$: p \u003e 0.25$$

Question 5

In hypothesis testing for a proportion, which method is recommended for determining statistical significance?

Accepted Answer

P-value method

Question 6

If you are given $$p = 0.10$$, $$n = 362$$, and $$x = 33$$, what is the sample proportion $$\hat{p}$$?

Accepted Answer

$$\hat{p} = \dfrac{33}{362} \approx 0.091$$

Question 7

When using the normal approximation to the binomial, which conditions must be satisfied for the approximation to be valid?

Accepted Answer

$$np \geq 5$$ and $$nq \geq 5$$

Question 8

A researcher wants to test $$H_0$$: p = 0.5$$ against H_1$: p 
eq 0.5$$ using a sample of $$n = 100$$ and $$x = 45. $$What type of test should be used?

Accepted Answer

Two-tailed test

Question 9

Which formula is used to compute the number of successes $$x$$ when only $$p$$ and $$n$$ are given?

Accepted Answer

$$x = np$$

Question 10

If the calculated P-value is less than the significance level $$\alpha$$, what is the correct conclusion?

Accepted Answer

Reject the null hypothesis $$H_0$$

Question 11

In the context of testing claims about a proportion, what does the confidence interval method provide?

Accepted Answer

An interval estimate for the population proportion

Question 12

Which of the following statements about the exact binomial method is TRUE?

Accepted Answer

It does not require $$np \geq 5$$ and $$nq \geq 5$$ for validity.

Question 13

What is the purpose of the simple continuity correction when using the normal approximation to the binomial?

Accepted Answer

To adjust for the discrete nature of the binomial distribution when approximating with a continuous normal distribution.

Question 14

A fast food restaurant wants to test if the rate of inaccurate orders is equal to 10%. In a sample of 362 orders, 33 were inaccurate. What is the value of $$np$$ and $$nq$$ for $$p = 0.10$$?

Accepted Answer

$$np = 36.2$$, $$nq = 325.8$$

Question 15

When using the critical value method for a right-tailed test at $$\alpha = 0.05$$, what is the critical value of $$z$$?

Accepted Answer

$$z = 1.645$$

Question 16

In a two-tailed test, how is the P-value calculated using the simple continuity correction?

Accepted Answer

Twice the smaller of the left or right-tailed P-values

Question 17

A survey finds that 2703 out of 5100 respondents said 'yes' to a question. What is the sample proportion $$\hat{p}$$?

Accepted Answer

$$\hat{p} = \dfrac{2703}{5100} \approx 0.530$$

Question 18

Which of the following is a correct interpretation of a P-value of 0.017 in a right-tailed test with $$\alpha = 0.05$$?

Accepted Answer

There is sufficient evidence to reject the null hypothesis.

Question 19

Why might the confidence interval method and the P-value method lead to different conclusions in hypothesis testing for a proportion?

Accepted Answer

Because the confidence interval method estimates a range for the proportion, while the P-value method tests a specific hypothesis.

Testing Claims about a Proportion (Normal Approximation to Binomial)

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