Answered: In a survey of 444 HIV-positive…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question 3: Quit smoking: In a survey of 444 HIV-positive smokers, 187 reported that they had used a nicotine patch to try to quit smoking. Can you conclude that less than half of HIV-positive smokers have used a nicotine patch? Use the a=0.05 level of significance and the P-value method with the TI-84 Plus calculator.

Part 1: State the appropriate null and alternate hypotheses.

H0:

H1:

This hypothesis test is a (BLANK) test.

Part 2: Compute the value of the test statistic. Round the answer to at least two decimal places.

z=(BLANK)

Part 3: Compute the P-value. Round the answer to at least four decimal places.

P-value: (BLANK)

Part 4: Determine whether to reject H0.

At the a=0.05 level, ▼Answer Choice the null hypothesis H0 .

Answer Choice:

Reject
Do Not Reject

Part 5: Using a=0.05, can you conclude that less than half of HIV-positive smokers have used a nicotine patch?

At the a=0.05 level of significance, there ▼Answer Choice enough evidence to conclude that less than half of HIV-positive smokers have used a nicotine patch.

Is
Is Not

Question 6: Mercury pollution: Mercury is a toxic metal that is used in many industrial applications. Eight measurements, in milligrams per cubic meter, were taken of the mercury concentration in a lake, with the following results. Assume that the population of measurements is approximately normally distributed.

0.99

1.01

1.02

0.94

0.93

1.00

0.96

0.98

Sample size: 8

Sample mean: 0.979

Sample standard deviation: 0.033

Can you conclude that the mean concentration is less than 1 milligram per cubic meter? Use the a =0.05 level of significance.

H0: μ=1

H1:μ< 1

Part 1: (a) Find the P-value. Round your answer to four decimal places if necessary.

The P-value is (BLANK)

Part 2: (b) What is the decision?

A. Reject H0

B. Do Not Reject H0

Part 3: (c) Interpret the result.

We ▼(Choose one) enough evidence at the 0.05 level of significance to conclude that mean concentration is less than 1 milligram per cubic meter.

Answer Choices:

A.Have

B. Do Not Have

Question 12: Spam: A researcher reported that 71.8% of all email sent in a recent month was spam. A system manager at a large corporation believes that the percentage at his company may be 68% . He examines a random sample of 500 emails received at an email server, and finds that 361 of the messages are spam. Can you conclude that the percentage of emails that are spam is greater than 68%? Use both a=0.10 and a=0.01 levels of significance and the P-value method with the TI-84 Plus calculator.

Part 1: State the appropriate null and alternate hypotheses.

H0:

H1:

This hypothesis test is a (BLANK) test.

Part 2: Compute the value of the test statistic. Round the answer to at least two decimal places.

z=(BLANK)

Part 3: Compute the P-value. Round the answer to at least four decimal places.

P-value: (BLANK)

Part 4: (d) Determine whether to reject H0.

At the a=0.10 level, ▼(Choose one) the null hypothesis H0.
At the a=0.01 level, ▼(Choose one) the null hypothesis H0.

Part 5: (e) State a conclusion.

At the a=0.10 level of significance, there▼(Choose one) enough evidence to conclude that greater than 68% of emails are spam.
At the a=0.01 level of significance, there▼(Choose one) enough evidence to conclude that greater than 68% of emails are spam.

Answer Choice:

Is
Is Not

Question 14: Big houses: The U.S. Census Bureau reported that the mean area of U.S. homes built in 2018 was 2559 square feet. Assume that a simple random sample of 22 homes built in 2020 had a mean area of 2654 square feet, with a standard deviation of 184 square feet. Assume the population of areas is normally distributed. Can you conclude that the mean area of homes built in 2020 is greater than that of homes built in 2018 ? Use the a=0.01 level of significance.

Part 1: (a) Find the P -value. Use the TI-84 calculator and round your answer to at least four decimal places.

The P-value is (BLANK)

Part 2: (b) What is the decision?

A. Reject H0

B. Do Not Reject H0

Part 3: (c) Interpret the result.

We ▼(Choose one) enough evidence at the 0.01 level of significance to conclude that the mean area of homes built in 2020▼(Choose one) that of homes built in 2018.

Answer Choice:

Have
Do Not Have

Answer Choice:

Is greater than
Is not equal to

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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