Q: If you want to test whether the average data use for smartphone users has changed from 1.8 GB/month, which hypotheses should you use?

$$H_0$$: \mu = 1.8$$, H_1$: \mu \neq 1.8$$

Question 1

Which of the following best describes a Type I error in the context of hypothesis testing?

Accepted Answer

Rejecting the null hypothesis when it is true.

Question 2

A pharmaceutical company is testing a new drug. The null hypothesis is that the drug has no effect or is harmful. What is the consequence of a Type II error in this scenario?

Accepted Answer

The company fails to approve a beneficial drug.

Question 3

Given a one-tail upper test with $$\alpha = 0.05$$, what is the critical z-score you should use to determine the rejection region?

Accepted Answer

$$1.645$$

Question 4

Suppose you are testing $$H_0$$: \mu = 100$$ versus H_1$: \mu 
eq 100$$ with $$\alpha = 0.05$$ and a sample size of $$n = 36. $$The population standard deviation is known to be $$\sigma = 12. If $$your sample mean is $$\bar{x} = 104$$, what is the value of the test statistic?

Accepted Answer

$$z = \frac{104 - 100}{12/\sqrt{36}} = \frac{4}{2} = 2$$

Question 5

In a two-tail hypothesis test with $$\alpha = 0.02$$ and $$n = 10$$, what are the critical t-values you should use?

Accepted Answer

$$\pm 2.821$$

Question 6

A sample of 350 cell phone users finds that 238 have 4G contracts. If last year’s proportion was $$p = 0.62$$, what is the sample proportion $$\hat{p}$$?

Accepted Answer

$$\hat{p} = \frac{238}{350} = 0.68$$

Question 7

Which formula should you use to calculate the z-test statistic for a population proportion?

Accepted Answer

$$z_p = \frac{\hat{p} - p}{\sqrt{\frac{p(1-p)}{n}}}$$

Question 8

If the p-value for your test is $$0.03$$ and $$\alpha = 0.05$$, what is the correct conclusion?

Accepted Answer

Reject $$H_0$$

Question 9

Which of the following will decrease both the probability of a Type I error ($$\alpha) $$and a Type II error ($$\beta) $$simultaneously?

Accepted Answer

Increasing the sample size

Question 10

A hotel chain wants to test if the average nightly rate in Chicago is less than $$188. A sample of 25 hotels yields $$\bar{x} = 177.5$$ and s = 25.4$. What is the t-test statistic?

Accepted Answer

$$t = \frac{177.5 - 188}{25.4/\sqrt{25}} = \frac{-10.5}{5.08} = -2.07$$

Question 11

In hypothesis testing, what does the power of a test represent?

Accepted Answer

The probability of correctly rejecting a false null hypothesis

Question 12

Which of the following is a correct statement about the relationship between $$\alpha$$ and $$\beta$$ for a fixed sample size?

Accepted Answer

As $$\alpha$$ increases, $$\beta$$ decreases.

Question 13

A two-tail hypothesis test is being conducted at $$\alpha = 0.05. $$What is the rejection region for the z-test statistic?

Accepted Answer

$$|z| \u003e 1.96$$

Question 14

If you want to test whether the average data use for smartphone users has changed from 1.8 GB/month, which hypotheses should you use?

Accepted Answer

$$H_0$$: \mu = 1.8$$, H_1$: \mu 
eq 1.8$$

Question 15

Which of the following is a necessary condition for using the normal approximation in hypothesis testing for a population proportion?

Accepted Answer

$$np \geq 5$$ and $$n(1-p) \geq 5$$

Question 16

A sample of 49 smartphone users has a mean data use of 1.86 GB/month. The population standard deviation is 0.20 GB. Test $$H_0$$: \mu = 1.8$$ vs H_1$: \mu 
eq 1.8 at$$ $$\alpha = 0.05. $$What is the test statistic?

Accepted Answer

$$z = \frac{1.86 - 1.8}{0.20/\sqrt{49}} = \frac{0.06}{0.0286} = 2.10$$

Question 17

If the calculated test statistic for a one-tail upper test is $$z = 1.44$$ and the critical value is $$z_{\alpha} = 1.645$$, what is the correct decision?

Accepted Answer

Do not reject $$H_0$$

Question 18

Which Excel function can be used to find the area to the left of a z-score for hypothesis testing?

Accepted Answer

=NORM.S.DIST(z, TRUE)

Question 19

In the context of quality control, what is the producer’s risk?

Accepted Answer

Type I error

Hypothesis Testing for a Single Population: Comprehensive Study Notes

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