# Find the rejection region appropriate for this test if we are using a significance level of 0.05

Question 1

A consumer product magazine recently ran a story concerning the increasing prices of digital cameras. The story stated that digital camera prices dipped a couple of years ago, but now are beginning to increase in price because of added features. According to the story, the average price of all digital cameras a couple of years ago was \$215.00. A random sample of n = 22 cameras was recently taken and entered into a spreadsheet. It was desired to conduct a test to determine if that average price of all digital cameras is now more than \$215.00. Find the rejection region appropriate for this test if we are using a significance level of 0.05. Assume camera prices are normally distributed.

Reject H0 if t > 1.717

Reject H0 if t > 2.080

Reject H0 if t < -2.080 or t > 2.080

Reject H0 if t > 1.960

Reject H0 if t > 1.721

Question 2

In a sample of 1600 computers, 344 were fournd to contain some form of malware. Find the margin of error for a 90% confidence interval estimating the true proportion of computers with malware.

0.0131

0.0169

0.0265

0.0201

0.0239

Question 3

A large electric utility claims that 80 percent of their customers are very satisfied with the service they receive. To test this claim, the local newspaper surveyed 200 customers. The results of the study are shown in the printout below.

One-Sample Z Test

Null Hypothesis: p = 0.8
Alternative Hyp: p ≠ 0.8

95% Conf Interval

Variable      p-hat  SE     Lower    Upper    Z      P
Satisfaction  0.735  0.028  0.674    0.796    -2.30  0.0214

Cases Included 200

Based on these findings, can we reject the electric utility’s claim that 80% of their customers are very satisfied? Using the above software output and a 5% significance level, what is the test’s conclusion?

H0 is not rejected. There is insufficient evidence to reject the claim that 80 percent of customers are very satisfied with the service they receive.

H0 is rejected. There is sufficient evidence to reject the claim that 80 percent of customers are very satisfied with the service they receive.

H0 is rejected. There is insufficient evidence to reject the claim that 80 percent of customers are very satisfied with the service they receive.

H0 is not rejected. There is sufficient evidence to reject the claim that 80 percent of customers are very satisfied with the service they receive.

Question 4

The Golden Comet is a hybrid chicken that is prized for its high egg production rate and gentle disposition. According to recent studies, the mean rate of egg production for 1-year-old Golden Comets is 5.4 eggs/week.

Sarah has 44 1-year-old hens that are fed exclusively on natural scratch feed: insects, seeds, and plants that the hens obtain as they range freely around the farm. Her hens exhibit a mean egg-laying rate of 5.8 eggs/day.

Sarah wants to determine whether the mean laying rate μ for her hens is higher than the mean rate for all Golden Comets. State the appropriate null and alternate hypotheses.

H0μ = 5.4, H1μ > 5.4

H0μ = 5.8, H1μ > 5.8

H0μ > 5.4, H1μ = 5.4

H0μ > 5.8, H1μ = 5.8

Question 5

Express the confidence interval (-1.22, 2.76) calculated for an unknown population mean μ in the form of point estimate ± margin of error.

0.77 ± 1.99

1.99 ± 0.77

1.89 ± 0.77

0.77 ± 1.89

0.77 ± 1.79

Question 6

A test of  versus  is performed using a significance level of . The value of the test statistic is .

If the true value of p is 0.35, does the test conclusion result in a Type I error, a Type II error, or a Correct decision?

Type II error

Correct decision

Type I error

Question 7

What is the critical value zα/2 for a 75% confidence level?

1.25

0.67

2.24

1.15

1.96

Question 8

Estimate the P-value for a test of H0μ = 12 versus H1μ ≠ 12 with test value t = -2.61 and a sample size of 15.

0.01< P-value < 0.02

0.025 < P-value < 0.05

0.02 < P-value < 0.05

0.005 < P-value < 0.01

0.01 < P-value < 0.025

Question 9

Historically, 40% of students at a university live on campus. In a new survey conducted to see if the current rate differs from the previous one, 91 out of 250 students randomly surveyed reported that they live on campus. Find the test statistic value for a test of the claim.

-1.16

-1.20

-1.18

-1.22

-1.14

Question 10

A machine is used to fill cans with 500 grams of a product. Over time the machine has a tendency to stop short of dispensing a full 500 grams. The machine needs to be serviced when the mass of the product dispensed is significantly lower than 500 grams.

Suppose that the average amount dispensed by the machine for a sample of 50 cans is 498 grams. Is there sufficient evidence that the machine should be serviced? Find the P-value for the test. Assume a population standard deviation of 6 grams.

0.0091

0.0273

0.0364

0.0455

0.0182

Question 11

A random sample of 11 patients had an average incubation period for a virus of 5.1 days with a standard deviation of 2.3 days. Construct a 99% confidence interval for the true mean incubation period, μ, of the virus. Assume patient incubation periods are normally distributed.

(3.5, 6.7)

(3.7, 6.5)

(2.9, 7.3)

(4.0, 6.2)

(3.3, 6.9)

Question 12

A monthly income investment scheme exists that promises variable monthly returns. A study of 300 months’ returns with this scheme was conducted. The results of the study are shown in the printout below.

One-Sample Z Test

Null Hypothesis: μ = 180
Alternative Hyp: μ > 180

99% Conf Interval

Variable    Mean    SE     Lower    Upper    Z     P
Return      190.33  4.518  178.69   201.97   2.29  0.0110

Cases Included 300

An investor will invest in the scheme only if they are assured an average monthly return greater than \$180. Should they invest in this scheme? Using the above software output and α = 0.01, what is the test conclusion?

Invest in the scheme. There is sufficient evidence to support the conclusion that the average monthly return is greater than \$180.

Do not invest in the scheme. There is sufficient evidence to support the conclusion that the average monthly return is greater than \$180.

Do not invest in the scheme. There is insufficient evidence to support the conclusion that the average monthly return is greater than \$180.

Invest in the scheme. There is insufficient evidence to support the conclusion that the average monthly return is greater than \$180.

Question 13

A study is being conducted to estimate the proportion of students interested in taking a course in a new subject area. How large of a sample is needed in order to be 90% confident that the sample proportion will not differ from the true proportion by more than 2%?

1702

241

2401

3404

4802

Question 14

A new filament design is tested to see if lightbulbs using the design last longer than the current bulb’s lifetime of 1430 hours. A sample of 40 bulbs employing the new filament had an average lifetime of 1450 hours. Compute the test statistic value for a hypothesis test of  versus  where μ is the new bulb’s true average lifetime. Assume  hours.

1.57

1.96

1.69

1.74

1.83

Question 15

How many flights must be sampled to estimate the true mean delay time for a particular airline if we want 95% confidence that the sample mean is within 5 minutes of the true mean, and the population standard deviation is known to be 20 minutes?

27

87

107

44

62

Question 16

Some hesitation about the unthinking use of significance (hypothesis) tests is a sign of statistical maturity. Which one of the following statements regarding significance tests is actually true?

An important practical distinction should be made between a P-value of 0.049 and a P-value of 0.051.

Statistical significance is a formal measure of practical importance or signficance.

The null hypothesis can be rejected by chance alone even if the null hypothesis is true.

Failure to reject the null hypothesis is likely to occur if the sample size is too large.

One can legitimately test a hypothesis on the same data that first suggested that hypothesis.

Question 17

The nicotine amounts in milligrams of 8 randomly selected cigarettes of a certain brand are given below. Find a 95% confidence interval for the true mean nicotine content per cigarette for this brand. Assume cigarette nicotine amounts are normally distributed.

3.1     4.5     4.2     6.0     5.1     3.3     5.9     2.5

(3.14, 5.51)

(3.57, 5.08)

(3.24, 5.41)

(3.27, 5.38)

(3.42, 5.23)

Question 18

A researcher conducts a study to see if college students get the same amount of sleep as the average adult does, which is 7.25 hours of sleep. A sample of 27 college students shows an average amount of sleep of 6.75 hours with a standard deviation of 1.15 hours. Are college students getting the same amount of sleep as the average adult? Calculate the test statistic value and state its P-value for a test of this conjecture. Assume the population is normally distributed.

t = -2.26; 0.02 < P-value < 0.05

t = -2.26; 0.025 < P-value < 0.05

t = -2.26; 0.01 < P-value < 0.025

z = -2.26; P-value = 0.0238

z = -2.26; P-value = 0.0119

Question 19

A random sample of 75 boxes of a certain brand of cereal has a mean weight of  = 17.95 oz. Construct a 99% confidence interval for the mean weight, μ, of all boxes of cereal of this brand. Assume σ = 0.81 oz.

17.71 oz. < μ < 18.19 oz.

17.80 oz. < μ < 18.10 oz.

17.69 oz. < μ < 18.21 oz.

17.77 oz. < μ < 18.13 oz.

17.73 oz. < μ < 18.17 oz.

Question 20

In a survey of 229 customers, 68 said they like pepperoni on their pizza. Construct a 95% confidence interval for the true proportion of customers that like pepperoni on their pizza.