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Chapter 10: Q. 1 (page 600)

At Rachel’s 11th birthday party, eight girls were timed to see how long (in seconds) they could hold their breath in a

relaxed position. After a two-minute rest, they timed themselves while jumping. The girls thought that the mean difference

between their jumping and relaxed times would be zero. Test their hypothesis.

Short Answer

Expert verified

Since p- the value is greater than α=0.05,we cannot reject the hypothesis H0and we can conclude that it is insufficient

evidence to conclude that the average difference is not zero.

Step by step solution

01

Given Information 

We need to test the hypothesis

02

Explanation 

We can take X1-X2to represent the difference between jumping and relaxed time.

We want to test this hypothesis:

H0:μ1=μ2H1:μ1≠μ2

In order to test the hypothesis, we are using the Student's test.

03

Simplification 

We need to find the mean and stand deviation of both samples:

μ1=32.375,s1=9.620477μ2=30.625,s2=8.331309

The differences between jumping and relaxed times are given by:

5, 7, 2, 1, - 2, 2, 2 -3

The number of differences is α=1.75:

∑i-18(di-a)2=75.5

Standard deviation differences are:

8=1n-1∑i-18(di-a)2=75.57=3.284

The standard error is: SE=n8=1.161

We can find the value of the test statistic is:

t=μ1-μ2SE=1.507

04

Graphical Presentation 

Using the applet, we get that p-value is 0.17554:

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Most popular questions from this chapter

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.

Are standard deviations known or unknown?

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.

What is the test statistic?

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.

What conclusion can you draw about the juggling class?

Use the following information to answer the next five exercises. A researcher is testing the effects of plant food on plant growth. Nine plants have been given the plant food. Another nine plants have not been given the plant food. The heights of the plants are recorded after eight weeks. The populations have normal distributions. The following table is the result. The researcher thinks the food makes the plants grow taller.

Draw the graph of the p-value.

Weighted alpha is a measure of risk-adjusted performance of stocks over a period of a year. A high positive weighted alpha signifies a stock whose price has risen while a small positive weighted alpha indicates an unchanged stock price during the time period. Weighted alpha is used to identify companies with strong upward or downward trends. The weighted alpha for the top 30 stocks of banks in the northeast and in the west as identified by Nasdaq on May 24,2013 are listed in Table 10.6 and Table10.7, respectively

Is there a difference in the weighted alpha of the top 30 stocks of banks in the northeast and in the west? Test at a 5% significance level. Answer the following questions:

a. Is this a test of two means or two proportions?

b. Are the population standard deviations known or unknown?

c. Which distribution do you use to perform the test?

d. What is the random variable?

e. What are the null and alternative hypotheses? Write the null and alternative hypotheses in words and in symbols.

f. Is this test right, left, or two tailed?

g. What is the p-value?

h. Do you reject or not reject the null hypothesis?

i. At the ___ level of significance, from the sample data, there ______ (is/is not) sufficient evidence to conclude that ______.

j. Calculate Cohen’s d and interpret it
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