# 1.3: Two-Sample Practice

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- 6120

## 10.1 Comparing Two Independent Population Means

*Use the following information to answer the next 15 exercises:* Indicate if the hypothesis test is for

*Use the following information to answer the next three exercises:*A study is done to determine which of two soft drinks has more sugar. There are 13 cans of Beverage A in a sample and six cans of Beverage B. The mean amount of sugar in Beverage A is 36 grams with a standard deviation of 0.6 grams. The mean amount of sugar in Beverage B is 38 grams with a standard deviation of 0.8 grams. The researchers believe that Beverage B has more sugar than Beverage A, on average. Both populations have normal distributions.**16**.Are standard deviations known or unknown?

17.What is the random variable?

**18**.Is this a one-tailed or two-tailed test?

**19**.Is this a test of means or proportions?

**20**.State the null and alternative hypotheses.

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**10.8****44**.What is the random variable?

**45**.State the null and alternative hypotheses.

**46**.What is the test statistic?

**47**.At the 1% significance level, what is your conclusion?

Plant group Sample mean height of plants (inches) Population standard deviation Food 16 2.5 No food 14 1.5 Table \(\PageIndex{9}\) **48**.Is the population standard deviation known or unknown?

**49**.State the null and alternative hypotheses.

**50**.At the 1% significance level, what is your conclusion?

*Use the following information to answer the next five exercises.*Two metal alloys are being considered as material for ball bearings. The mean melting point of the two alloys is to be compared. 15 pieces of each metal are being tested. Both populations have normal distributions. The following table is the result. It is believed that Alloy Zeta has a different melting point.Sample mean melting temperatures (°F) Population standard deviation Alloy Gamma 800 95 Alloy Zeta 900 105 Table

**10.10****51**.State the null and alternative hypotheses.

**52**.Is this a right-, left-, or two-tailed test?

**53**.At the 1% significance level, what is your conclusion?

## 10.6 Matched or Paired Samples

*Use the following information to answer the next five exercises.*A study was conducted to test the effectiveness of a software patch in reducing system failures over a six-month period. Results for randomly selected installations are shown in Table \(\PageIndex{11}\). The “before” value is matched to an “after” value, and the differences are calculated. The differences have a normal distribution. Test at the 1% significance level.Installation A B C D E F G H Before 3 6 4 2 5 8 2 6 After 1 5 2 0 1 0 2 2 Table

54.**10.11**What is the random variable?

55.State the null and alternative hypotheses.

**56**.What conclusion can you draw about the software patch?

*Use the following information to answer next five exercises.*A study was conducted to test the effectiveness of a juggling class. Before the class started, six subjects juggled as many balls as they could at once. After the class, the same six subjects juggled as many balls as they could. The differences in the number of balls are calculated. The differences have a normal distribution. Test at the 1% significance level.Subject A B C D E F Before 3 4 3 2 4 5 After 4 5 6 4 5 7 Table \(\PageIndex{12}\) **57**.State the null and alternative hypotheses.

**58**.What is the sample mean difference?

**59**.What conclusion can you draw about the juggling class?

*Use the following information to answer the next five exercises.*A doctor wants to know if a blood pressure medication is effective. Six subjects have their blood pressures recorded. After twelve weeks on the medication, the same six subjects have their blood pressure recorded again. For this test, only systolic pressure is of concern. Test at the 1% significance level.Patient A B C D E F Before 161 162 165 162 166 171 After 158 159 166 160 167 169 Table

**10.13****60**.State the null and alternative hypotheses.

**61**.What is the test statistic?

**62**.What is the sample mean difference?

**63**.What is the conclusion?

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