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Chapter 9: Q 103. (page 610)

You are testing H0:渭=10against Ha:渭<10based on an SRS of20

observations from a Normal population. The t statistic is t=鈭�2.25

The P-value

a. falls between 0.01 and 0.02.

b. falls between 0.02 and 0.04.

c. falls between 0.04 and 0.05.

d. falls between 0.05 and 0.25.

e. is greater than 0.25.

Short Answer

Expert verified

The correct option is (a) falls between falls between 0.01 and 0.02

Step by step solution

01

Given information

Sample size(n)=20

Test statistic(t)=鈭�2.25

The null and alternative hypotheses are:

H0:渭=10Ha:渭<10

02

Explanation

According to the alternative hypothesis, the test is one-tailed.

The degree of freedom can be determined using the following formula:

Degreeoffreedom(df)=n鈭�1=20鈭�1=19

The p-value can be calculated as:

P鈭�value=P(t>|t|)=P(t>|鈭�2.25|)=0.018

Thus, it could be said that P-value lies between0.01and0.02

Hence, the correct option is (a).

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Most popular questions from this chapter

pg559炉

No homework Refer to Exercises 1 and 9. What conclusion would you make at the伪=0.05伪=0.05level?

Fair coin? You want to determine if a coin is fair. So you toss it 10times and record the proportion of tosses that land 鈥渉eads.鈥� You would like to perform a test of H0:p=0.5versus Ha:p鈮�0.5, where p= the proportion of all tosses of the

coin that would land 鈥渉eads.鈥� Check if the conditions for performing the significance test are met.

Better parking A local high school makes a change that should improve student satisfaction with the parking situation. Before the change, 37% of the school鈥檚 students approved of the parking that was provided. After the change, the principal surveys an SRS of students at the school. She would like to perform a test of H0:p=0.37Ha:p>0.37where p is the true proportion of students at school who are satisfied with the parking

situation after the change.

a. The power of the test to detect that p=0.45 based on a random sample of 200 students and a significance level of 伪=0.05 is 0.75 Interpret this value.

b. Find the probability of a Type I error and the probability of a Type II error for the test in part (a).

c. Describe two ways to increase the power of the test in part (a).

Tests and confidence intervals The P-value for a two-sided test of the null hypothesis H0:渭=10is0.06

a. Does the 95% confidence interval for 渭 include 10? Why or why not?

b. Does the 90% confidence interval for 渭 include 10? Why or why not?

A random sample of 100 likely voters in a small city produced 59 voters in favor of Candidate A. The observed value of the standardized test statistic for performing a test of H0:p=0.5H0:p=0.5versus Ha:p>0.5Ha:p>0.5

is which of the following?

a)z=0.59-0.50.59(0.41)100

b)z=0.59-0.50.5(0.5)100

c)z=0.5-0.590.59(0.41)100

d)z=0.5-0.590.5(0.5)100

e)z=0.59-0.5100
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