Quiz 5 Chapter 8

1. ​Claim: A  of adults would erase all of their personal information online if they could. A software firm survey of  550 randomly selected adults showed that 45​% of them would erase all of their personal information online if they could. Complete parts​ (a) and​ (b) below.

a. Express the original claim in symbolic form. Let the parameter represent the adults that would erase their personal information.

_________ (Type an integer or a decimal. Do not​ round.)

b. Identify the null and alternative hypotheses.
​

$H_1 : \_\_\_\_\_$

​(Type integers or decimals. Do not​ round.)

2.  Claim: The mean pulse rate​ (in beats per​ minute) of adult males is equal to 68.6 bpm. For a random sample of 140 adult​ males, the mean pulse rate is 70.1  bpm and the standard deviation is 11.1 bpm bpm. Complete parts​ (a) and​ (b) below.

a. Express the original claim in symbolic form

_________ (Type an integer or a decimal. Do not​ round.)

b. Identify the null and alternative hypotheses.

$H_0 : \_\_\_\_\_$

$H_1 : \_\_\_\_\_$

​(Type integers or decimals. Do not​ round.)

3. Claim: The standard deviation of pulse rates of adult males is more than 11 bpm  bpm. For a random sample of 139 adult​ males, the pulse rates have a standard deviation of 11.7 bpm. Complete parts​ (a) and​ (b) below.

a. Express the original claim in symbolic form

_________ (Type an integer or a decimal. Do not​ round.)

b. Identify the null and alternative hypotheses.

$H_0 : \_\_\_\_\_$

$H_1 : \_\_\_\_\_$

​(Type integers or decimals. Do not​ round.)

4.  Claim: Most adults would erase all of their personal information online if they could. A software firm survey of 402  randomly selected adults showed that 58​% of them would erase all of their personal information online if they could. Find the value of the test statistic.

The value of the test statistic is ____

5. Fill in the blank.  The​ _________ hypothesis is a statement that the value of a population parameter is equal to some claimed value.

6. Fill in the blank.  The​ ___________ is a value used in making a decision about the null hypothesis and is found by converting the sample statistic to a score with the assumption that the null hypothesis is true.

7.  Which of the following is NOT true about​ P-values in hypothesis​ testing?

Choose the correct answer below.

1. The​ P-value is an area. 
2. If the P is​ high, the null will fly. 
3. If the P is​ low, the null must go.
4. The​ P-value separates the critical region from the values that do not lead to rejection of the null hypothesis.   

8.  Which of the following is NOT a criterion for making a decision in a hypothesis​ test?
Choose the correct answer below.

1. If the test statistic falls within the critical​ region, the decision is to reject the null hypothesis. 
2. If ​P-value
   $\le a$

   ​, the decision is to reject the null hypothesis.​ Otherwise, we fail to reject the null hypothesis. 

3. If the​ P-value is less than​ 0.05, the decision is to reject the null hypothesis.​ Otherwise, we fail to reject the null hypothesis. 
4. If a confidence interval does not include a claimed value of a population​ parameter, the decision is to reject the null hypothesis.

9.  Thirty-three different video games showing drug use were observed. The duration times of  drug use ​(in seconds) were recorded. When using this sample for a t test of the claim that the population mean is greater than 81 ​sec, what does df​ denote, and what is its​ value?
What does df​ denote?

1. The sample standard deviation
2. The number of degrees of freedom
3. The test statistic
4. The sample size

The value of df is  ____ ​(Type an integer or a decimal. Do not​ round.)

10.  The display provided from technology available below results from using data for a smartphone​ carrier’s data speeds at airports to test the claim that they are from a population having a mean less than  Mbps. Conduct the hypothesis test using these results. Use a  significance level. Identify the null and alternative​ hypotheses, test​ statistic, P-value, and state the final conclusion that addresses the original claim.

Assuming all conditions for conducting a hypothesis test are​ met, what are the null and alternative​ hypotheses?

Identify the test statistic.

__________. ​(Round to two decimal places as​ needed.)

Identify the​ P-value.

__________. ​(Round to three decimal places as​ needed.)

State the final conclusion that addresses the original claim.

___________

.  There is  _______  evidence to support the claim that the sample is from a population with a mean less than ____  Mbps.

11.  A data set includes data from student evaluations of courses. The summary statistics are n = 89,

3.91, s = 0.64. Use a 0.05 significance level to test the claim that the population of student course evaluations has a mean equal to 4.00.  Assume that a simple random sample has been selected. Identify the null and alternative​ hypotheses, test​ statistic, P-value, and state the final conclusion that addresses the original claim.

What are the null and alternative​ hypotheses?

Determine the test statistic.  ________.  ​(Round to two decimal places as​ needed.)

Determine the​ P-value. __________. ​(Round to three decimal places as​ needed.)

State the final conclusion that addresses the original claim.

____________

There is _______ evidence to conclude that the mean of the population of student course evaluations is equal to 4.00 ________ correct.

12.  Listed below are the lead concentrations in

​g/g measured in different traditional medicines. Use a 0.05 significance level to test the claim that the mean lead concentration for all such medicines is less than 19

​g/g. Assume that the sample is a simple random sample.

4.5       16      16        12     13.5     19.5     13       17.5      15.5       17
 
 Assuming all conditions for conducting a hypothesis test are​ met, what are the null and alternative​ hypotheses?

Determine the test statistic.   _______ ​(Round to two decimal places as​ needed.)

Determine the​ P-value.   ______ ​(Round to three decimal places as​ needed.)

State the final conclusion that addresses the original claim.

________

There is  ______ evidence to conclude that the mean lead concentration for all such medicines is ______ 19

​g/g.

13.  A simple random sample of 41 men from a normally distributed population results in a standard deviation of 12.7 beats per minute. The normal range of pulse rates of adults is typically given as 60 to 100 beats per minute. If the range rule of thumb is applied to that normal​ range, the result is a standard deviation of 10 beats per minute. Use the sample results with a 0.10 significance level to test the claim that pulse rates of men have a standard deviation equal to 10 beats per minute. Complete parts​ (a) through​ (d) below.

a. Identify the null and alternative hypotheses. Choose the correct answer below.

b. Compute the test statistic.

${\chi }^2 =$

_____ ​(Round to three decimal places as​ needed.)

c. Find the​ P-value. 

P-value = ______ (Round to four decimal places as​ needed.)

d. State the conclusion.

___________

, because the​ P-value is _________ the level of significance. There is _______ evidence to warrant rejection of the claim that the standard deviation of​ men’s pulse rates is equal to 10 beats per minute.

14.  A simple random sample of 26 filtered​ 100-mm cigarettes is obtained from a normally distributed​ population, and the tar content of each cigarette is measured. The sample has a standard deviation of 0.22mg. Use a 0.05 significance level to test the claim that the tar content of filtered​ 100-mm cigarettes has a standard deviation different from 0.35 ​mg, which is the standard deviation for unfiltered​ king-size cigarettes. Complete parts​ (a) through​ (d) below.

a. What are the null and alternative​ hypotheses?

b. Find the test statistic.

${\chi }^2 =$

_______ ​(Round to three decimal places as​ needed.)

c. Find the​ P-value of the test statistic.

The​ P-value of the test statistic is _____.  ​(Round to three decimal places as​ needed.)

d. State the conclusion.

____________

.  There  _____ sufficient evidence to conclude that the tar content of filtered​ 100-mm cigarettes has a standard deviation different from 0.35 mg.