2. Suppose a company sells bacon in packages that they claim average a weight of 13 ounces. Timothy believes that the actual average weight of the packages is different than what the company claims, and would like to test this using a significance level of 0.02. He takes a random sample of 31 packages and gets a sample mean of 13.72 ounces and a sample standard deviation of 1.18 ounces. (a) What are the null and alternative hypotheses? H₀:

p / / p1 - p2 / 1 - 2

< / / > / =

13 / 13.72

H_A:

p / / p / 1 - p2 / 1 - 2

= / / / < / / >

13 / 13.72

(b) What is the test statistic? (Round your answer to 3 decimal places, if needed.) (c) Using the statistical table, the p-value is 0.01 < p-value < 0.02 / 0.02 < p-value < 0.05 / 0.05 < p-value < 0.10 / 0.10 < p-value < 0.20 / p-value > 0.20 / 0 < p-value < 0.01 . (d) Based on the p-value, Timothy should reject / fail to reject the null hypothesis. (e) This data provides / does not provide sufficient evidence to conclude that the actual average weight of the packages is less than / more than / different from what the company claims.

3. Best Buy claims that, across all their stores, the average price of a desktop computer in the past year was 1350 dollars. Darryl thinks that Best Buy is understating the true average price, so he decides to test this using a significance level of 0.1. He samples 31 computer prices and gets a sample mean of 1495 dollars and a sample standard deviation of 200 dollars. (a) What are the null and alternative hypotheses? H₀:

p / / p1 - p2 / 1 - 2

< / / > / =

1350 / 1495

H_A:

p / / p1 - p2 / 1 - 2

= / / / < / / >

1350 / 1495

(b) What is the test statistic? (Round your answer to 3 decimal places, if needed.) (c) Using the statistical table, the p-value is 0.005 < p-value < 0.01 / 0.01 < p-value < 0.025 / 0.025 < p-value < 0.05 / 0.05 < p-value < 0.10 / p-value > 0.10 / 0 < p-value < 0.005 . (d) Based on the p-value, Darryl should reject / fail to reject the null hypothesis. (e) This data provides / does not provide sufficient evidence to conclude that Best Buy is not understating /understating the true average price.

5. Scientists want to estimate the mean weight of mice after they have been fed a special diet. From previous studies, it is known that the weight is normally distributed with a standard deviation of 5 grams. What is the minimum required sample size if the scientists wish to estimate the true mean to within 0.1 grams with 95% confidence? (Round to the appropriate integer.) Answer: n =

6. Megan would like to test whether the average commute time is noticeably different for students at two different high schools in her city, using a significance level of 0.02. In a sample of 41 students at High School 1, she gets a sample mean of 21.3 minutes and a sample standard deviation of 3.1 minutes. In a sample of 61 students at High School 2, she gets a sample mean of 17.8 minutes and a sample standard deviation of 4.8 minutes. Assume the population variances are equal. (a) What are the null and alternative hypotheses? H₀:

p / / p1 - p2 / 1 - 2 / d

< / / > / =

0 / 3.5

H_A:

p / / p1 - p2 / 1 - 2 / d

= / / / < / / >

0 / 3.5

(b) What is the test statistic? (Round your answer to 3 decimal places, if needed.) (c) Using the statistical table, the p-value is 0.01 < p-value < 0.02 / 0.02 < p-value < 0.05 / 0.05 < p-value < 0.10 / 0.10 < p-value < 0.20 / p-value > 0.20 / 0 < p-value < 0.01 . (d) Based on the p-value, Megan should reject / fail to reject the null hypothesis. (e) This data provides / does not provide sufficient evidence to conclude that the average commute time for students at High School 1 is less than / more than / different from the average commute time for students at High School 2.

7. A study was carried out at an Edmonton hospital to compare two different methods of care management of geriatric patients who were transferred from the emergency room to the geriatric ward. The two methods were "usual care" and "geriatric team care." The assignment of patients to the two groups was done at random; 38 were assigned to the "usual care" group (control group, C) and 39 to the "geriatric team care" group (treatment group, T). The researcher is interested in carrying out a hypothesis test to see if the average hospitalization cost for the "geriatric team care" is less than that for the "usual care" at the significance level of 0.02. The sample mean hospitalization cost for the control group is 3805 dollars with a sample standard deviation of 1010 dollars. The sample mean hospitalization cost for the "geriatric team care" is 2595 dollars with a sample standard deviation of 1220 dollars. (a) What are the null and alternative hypotheses? H₀:

p / / pC - pT / C - T / d

< / / > / =

0 / 1210

H_A:

p / / pC - pT / C - T / d

= / / / < / / >

0 / 1210

(b) What is the test statistic? (Round your answer to 3 decimal places, if needed.) (c) Using the statistical table, the p-value is 0.005 < p-value < 0.01 / 0.01 < p-value < 0.025 / 0.025 < p-value < 0.05 / 0.05 < p-value < 0.10 / p-value > 0.10 / 0 < p-value < 0.005 . (d) Based on the p-value, the researcher should reject fail to reject the null hypothesis. (e) This data provides / does not provide sufficient evidence to conclude that the average hospitalization cost for the "geriatric team care" is less than / greater than / different from the average hospitalization cost for "usual care".

8. Edward would like to test whether the average price of a pair of jeans at Pauline's Pants (group 1) is greater than the average price of a pair of jeans at Frank's Fashion (group 2). In a sample of 41 pairs of jeans at Pauline's Pants, he gets a sample mean of 76 dollars, and a sample standard deviation of 3.4 dollars. In a sample of 41 pairs of jeans at Frank's Fashion, he gets a sample mean of 72 dollars, and a sample standard deviation of 7.5 dollars. Assume population variances are unequal and use a significance level of 0.01. (a) What are the null and alternative hypotheses? H₀:

p / / p1 - p2 / 1 - 2 / d

< / / > / =

0 / 4

H_A:

p / / p1 - p2 / 1 - 2 / d

= / / / < / / >

0 / 4

(b) What is the test statistic? (Round your answer to 3 decimal places, if needed.) (c) Using the statistical table, the p-value is 0.005 < p-value < 0.01 / 0.01 < p-value < 0.025 / 0.025 < p-value < 0.05 / 0.05 < p-value < 0.10 / p-value > 0.10 / 0 < p-value < 0.005 . (d) Based on the p-value, Edward should reject / fail to reject the null hypothesis. (e) This data provides / does not provide sufficient evidence to conclude that the average price of a pair of jeans at Pauline's Pants is less than / greater than / different from the average price of a pair of jeans at Frank's Fashion.

9. Do skiers spend less than golfers on their vacations? To help answer this question, a travel agency surveyed 61 customers who regularly take their partners on a skiing vacation and 61 customers who regularly take their partners on a golf vacation. The amounts spent on vacations last year are shown in the following table. Perform an appropriate hypothesis test and use a significance level of 0.05.

	n	Average	Standard deviation
Skiers (S)	61	2666	315
Golfers (G)	61	3214	657
Difference (d = S - G)	61	-548	554

(a) What are the null and alternative hypotheses? H₀:

p / / pS - pG / S - G / d

< / / > / =

0 / -548

H_A:

p / / pS - pG / S - G / d

= / / / < / / >

0 / -548

(b) What is the test statistic? (Round your answer to 3 decimal places, if needed.) (c) Using the statistical table, the p-value is 0.005 < p-value < 0.01 / 0.01 < p-value < 0.025 / 0.025 < p-value < 0.05 / 0.05 < p-value < 0.10 / p-value > 0.10 / 0 < p-value < 0.005 . (d) Based on the p-value, the travel agency should reject / fail to reject the null hypothesis. (e) This data provides / does not provide sufficient evidence to conclude that the skiers spend, on average, less than / more than / the same amount as golfers on their vacations.

14. In a study, temperature readings were taken at different locations in 1961 and in 2015. The average daily temperatures for the month of June in each of 36 different locations are listed below. We would like to see if there is any difference between the mean temperatures of 1961 and 2015. If you believe the populations are independent, then assume the population variances are equal.

Location	n	Average	Standard deviation
1961	36	83	12.4
2015	36	87	9.8
Difference (d = y1961 - y2015)	36	-4.0	5.3

Perform a statistical test. (a) What are the null and alternative hypotheses? H₀:

p / / p1961 - p2015 / 1961 - 2015 / d

< / / > / =

0 / -4.0

H_A:

p / / p1961 - p2015 / 1961 - 2015 / d

= / / / < / / >

0 / -4.0

(b) What is the test statistic? (Round your answer to 3 decimal places, if needed.) (c) Using the statistical table, the p-value is 0.01 < p-value < 0.02 / 0.02 < p-value < 0.05 / 0.05 < p-value < 0.10 / 0.10 < p-value < 0.20 / p-value > 0.20 /0 < p-value < 0.01 . (d) Based on the p-value, reject /fail to reject the null hypothesis at the significance level of 0.02. (e) This data provides / does not provide sufficient evidence to conclude that the mean temperature in 1961 is less than / more than / different from the mean temperature in 2015.