Questions
You wish to test the claim that the first population mean is less than the second...

You wish to test the claim that the first population mean is less than the second population mean at a significance level of α=0.02α=0.02.     

Ho:μ1=μ2Ho:μ1=μ2
Ha:μ1<μ2Ha:μ1<μ2

You obtain the following two samples of data.

Sample #1 Sample #2
72.8
86.5
83.4
79.7
88.0
76.7
86.5
87.5
93.6
91.3
82.0
78.6
92.7
89.2
95.0
63.1
82.9
82.0
104.1
75.4
84.2
98.6
60.6
76.4
85.9
83.7
75.9
74.8
  1. What is the test statistic for this sample?

    test statistic =  Round to 3 decimal places.
  2. What is the p-value for this sample?

    p-value =  Use Technology Round to 4 decimal places.
  3. The p-value is...
    • less than (or equal to) αα
    • greater than αα

  4. This test statistic leads to a decision to...
    • reject the null
    • accept the null
    • fail to reject the null

  5. As such, the final conclusion is that...
    • There is sufficient evidence to warrant rejection of the claim that the first population mean is less than the second population mean.
    • There is not sufficient evidence to warrant rejection of the claim that the first population mean is less than the second population mean.
    • The sample data support the claim that the first population mean is less than the second population mean.
    • There is not sufficient sample evidence to support the claim that the first population mean is less than the second population mean.

In: Statistics and Probability

A survey found that 25% of consumers from a Country A are more likely to buy...

A survey found that 25% of consumers from a Country A are more likely to buy stock in a company based in Country​ A, or shop at its​ stores, if it is making an effort to publicly talk about how it is becoming more sustainable. Suppose you select a sample of 200 respondents from Country A. Complete parts​ (a) through​ (d) below.

  1. ​ What is the probability that in the​ sample, fewer than 25% are more likely to buy stock in a company based in Country​ A, or shop at its​ stores, if it is making an effort to publicly talk about how it is becoming more​ sustainable?

The probability is __%?

(Round to two decimal places as needed)

  1. What is the probability that in the​ sample, between 20​% and 30​% are more likely to buy stock in a company based in Country​ A, or shop at its​ stores, if it is making an effort to publicly talk about how it is becoming more​ sustainable?

The probability is __%?

(Round to two decimal places as needed)

  1. What is the probability that in the​ sample more than 20​% are more likely to buy stock in a company based in Country​ A, or shop at its​ stores, if it is making an effort to publicly talk about how it is becoming more​ sustainable?

The probability is __%?

(Round to two decimal places as needed)

  1. If a sample of 800 is taken, how does this change you answers to (a) through (c)

If a sample of 800 is taken, what is the probability that in the​ sample, fewer than 25% are more likely to buy stock in a company based in Country​ A, or shop at its​ stores, if it is making an effort to publicly talk about how it is becoming more​ sustainable?

The probability is __%?

(Round to two decimal places as needed)

If a sample of 800 is taken, what is the probability that in the​ sample, between 20​% and 30​% are more likely to buy stock in a company based in Country​ A, or shop at its​ stores, if it is making an effort to publicly talk about how it is becoming more​ sustainable?

The probability is __%?

(Round to two decimal places as needed)

If a sample of 800 is taken, what is the probability that in the​ sample more than 20​% are more likely to buy stock in a company based in Country​ A, or shop at its​ stores, if it is making an effort to publicly talk about how it is becoming more​ sustainable?

The probability is __%?

(Round to two decimal places as needed)

In: Statistics and Probability

A systems specialist has studied the workflow of clerks doing the same inventory work. Based on...

A systems specialist has studied the workflow of clerks doing the same inventory work. Based on this study, she designed a new workflow layout for the inventory system. To compare average production for the old and new methods, six clerks were randomly selected for the study. The average production rate for each clerk was recorded before and after the new system was introduced. The results are shown below. Test the claim that the new system is different in the mean number of items processed per shift. Use α = .05.

Clerk Joe Jon Joy Jen Jan Job

Old 123 114 112 82 127 122

New 116 108 93 88 119 111

a. State the null and alternative hypotheses (2 point)
b. Write the formula you will use in the space below: (1 point)
c. Identify all variables and corresponding values from the formula. (2 points)
d. Calculate the test statistic. (2 points) e. What is the critical value? (1 point) _________________
f. Interpret your result within the context of the problem. (2 points)

In: Statistics and Probability

High in the Rocky Mountains, a biology research team has drained a lake to get rid...

High in the Rocky Mountains, a biology research team has drained a lake to get rid of all fish. After the lake was refilled, they stocked it with an endangered species of Greenback trout. Of the 2000 Greenback trout put into the lake 600 were tagged for later study. An electroshock method is used on individual fish to get a study sample. However, this method is hard on the fish. The research team wants to know the smallest number of fish that must be electroshocked to be at least 90% sure of getting a sample of two or more tagged trout.

In: Statistics and Probability

Suppose that scores on a test are normally distributed with a mean of 80 and a...

Suppose that scores on a test are normally distributed with a mean of 80 and a standard deviation of 8. Determine the score that would be considered the first/lower quartile (??)

In: Statistics and Probability

You are opening your own wedding planning business and are conducting some market research. According to...

You are opening your own wedding planning business and are conducting some market research. According to The Knot Real Weddings Study, the average cost of a wedding in the U.S. is $35,000.

You are skeptical about whether these numbers apply to the Piedmont Triad area—your target market—and so you decide to conduct your own survey. After randomly sampling 40 recently married couples, you find an average cost of $32,000 with a standard deviation of $10,000.

1. Find the 90% confidence interval for the mean wedding cost in the Piedmont Triad.

a. What is the point estimate of the mean wedding cost for the Piedmont Triad?

b. Find the standard error of the mean.

c. Find the critical value. (You’ll need to decide whether to use a z-score or a t-score.)

d. Put it together to find the confidence interval.

2. What is the margin of error for the 90% confidence interval?

3. Interpret the 90% confidence interval for the mean wedding cost in the Piedmont Triad. Does the interval include the average for the U.S.? Would you conclude that the cost of weddings in the Piedmont Triad is different from the rest of the U.S.?

4. Find the 95% confidence interval for the mean wedding cost for the Piedmont Triad. How does it compare to the 90% confidence interval (narrower or wider)? Does your conclusion about the Piedmont Triad being different change?

5. Suppose you wanted to keep the confidence level at 90%, but you wanted to decrease the width of the interval. How could you do this?

6. When you conduct your survey, you also ask whether the couple had a destination wedding. Seven out of the 40 couples reported having a destination wedding. Find the 80% confidence interval for the proportion of couples that have a destination wedding.

a. What is the point estimate of the proportion of destination weddings for the Piedmont Triad

b. Find the standard error of the proportion.

c Find the critical value.

d. Put it together to find the confidence interval.

7. You find out that respondents to The Knot’s survey were recruited from members of TheKnot.com. Do you trust that the survey results come from a representative sample? Why or why not?

In: Statistics and Probability

Two factors, time and medium are investigated on bacterial count on specimens. The response values are...

Two factors, time and medium are investigated on bacterial count on specimens. The response values are given.

a. Perform a factorial analysis using the EXCEL spreadsheet.

b. Create a factorial design square

c. Draw the main effects plot

d. Give conclusions

Medium

time 10

time 15

time 20

1

2.6

4.0

5.5

1

2.7

4.1

5.4

2

3.7

5.7

7.8

2

3.8

5.8

7.7

In: Statistics and Probability

1. The maximum acceptable level of a certain toxic chemical in vegetables has been set at...

1. The maximum acceptable level of a certain toxic chemical in vegetables has been set at 0.4 parts per million (ppm). A consumer health group measured the level of the chemical in a random sample of tomatoes obtained from one producer. The levels, in ppm, are shown below.

0.31 0.47 0.19 0.72 0.56

0.91 0.29 0.83 0.49 0.28

0.31 0.46 0.25 0.34 0.17

0.58 0.19 0.26 0.47 0.81

Do the data provide sufficient evidence to support the claim that the mean level of the chemical in tomatoes from this producer is greater than the recommended level of 0.4 ppm? Use a 0.05 significance level to test the claim that these sample levels come from a population with a mean greater than 0.4 ppm. Use the P-value method of testing hypotheses. The population standard deviation is unknown.

options are:

a) P-value: p = 0.0435 Because p < alpha, we reject the null hypothesis. There is sufficient evidence to support the claim that u>0.4ppm

b) P-value: p = 0.8035 Because p > alpha, we fail to reject the null hypothesis. There is not sufficient evidence to support the claim that u>0.4ppm

c) P-value: p = 0.1965 Because p > alpha, we fail to reject the null hypothesis. There is not sufficient evidence to support the claim that u>0.4ppm

d) P-value: p = 0.3929 Because p > alpha, we fail to reject the null hypothesis. There is not sufficient evidence to support the claim that u>0.4ppm

In: Statistics and Probability

1) Describe and elaborate upon the following (a) A beta distribution (b) A joint probability density...

1) Describe and elaborate upon the following

(a) A beta distribution

(b) A joint probability density function

(c) A marginal probability density function

(d) A conditional probability density function

(e) Covariance and correlation between two random variables

In: Statistics and Probability

Vehicle speed on a particular bridge in China can be modeled as normally distributed? If 5%...

Vehicle speed on a particular bridge in China can be modeled as normally distributed?

If 5% of all vehicles travel less than 39.18 m/h and 10% travel more than 73.27 m/h, what are the mean and standard deviation of vehicle speed? (Round your answers to three decimal places.)

a) mean?

standard deviation?

b) What is the probability that a randomly selected vehicle's speed is between 50 and 65 m/h? (Round your answer to four decimal places.)

c) What is the probability that a randomly selected vehicle's speed exceeds the speed limit of 70 m/h? (Round your answer to four decimal places.)

You may need to use the appropriate table in the Appendix of Tables to answer this question.

In: Statistics and Probability

For this assignment, you will review two different situations that both involve comparing a sample to...

For this assignment, you will review two different situations that both involve comparing a sample to a population. Consider the information available for each situation, choose the correct test, and use the data to conduct it.

A researcher wants to compare the email use of the employees at one company to the corresponding population. Data is collected on the number of emails received by the company's employees. It will be necessary to use this sample data, as well as population data to determine if there is a significant difference between both.
Population
Mean number of emails: 25
Standard deviation: 3
Sample
Mean number of emails: 20
Total employees: 100
A researcher wants to compare the number of vehicles owned by families in one location to the larger population. Data is collected on the number of vehicles owned by each family. It will be necessary to use this sample data, as well as population data to determine if there is a significant difference between them.
Population
Mean number of vehicles: 4
Sample
Mean number of vehicles: 3
Standard deviation: 1
Sample size: 100
Create a report of approximately 1-2 pages in which you address the following:

Identify the test you selected for each situation.
Explain why it was the appropriate test.
Present the results of each test.
Explain whether or not a significant difference was found between the sample and the population.

In: Statistics and Probability

What is Best fit distribution for this data/ Customer Arrival time (mins) 1 1 2 4...

What is Best fit distribution for this data/

Customer Arrival time (mins)
1 1
2 4
3 3
4 0
5 0
6 1
7 3
8 3
9 2
10 0
11 3
12 1
13 2
14 0
15 2
16 0
17 1
18 2
19 3
20 2
21 3
22 0
23 2
24 3
25 3
26 0

In: Statistics and Probability

The owner of Showtime Movie Theaters, Inc., used multiple regression analysis to predict gross revenue ()...

The owner of Showtime Movie Theaters, Inc., used multiple regression analysis to predict gross revenue () as a function of television advertising () and newspaper advertising ().

Weekly Gross Revenue
(s)
Televison Advertising
(s)
Newspaper Advertising
(s)
97 6 2.5
90 3 2
95 5 2.5
92 2.5 3.5
96 3 4.3
94 3.5 3.3
95 3.5 4.2
95 4 3.5

The estimated regression equation was .

The computer solution provided .

a. Compute  (to 3 decimals).

Compute  (to 3 decimals).

b. When television advertising was the only independent variable,  and . Are the multiple regression analysis results preferable?

- Select your answer -No, because less variability is explained when both independent variables are usedYes, because greater variability is explained when both independent variables are usedItem 3

In: Statistics and Probability

Perform the following tasks on R Studio Construct a function called conv1 which inputs a measurement...

Perform the following tasks on R Studio
Construct a function called conv1 which inputs a measurement in centimeters and outputs the corresponding measurement in inches and construct another function called conv2 which inputs a measurement in centimeters and outputs the corresponding measurements in inches, feet, and meters

In: Statistics and Probability

Question 11 (1 point) Saved A USA Today article claims that the proportion of people who...

Question 11 (1 point)

Saved

A USA Today article claims that the proportion of people who believe global warming is a serious issue is 0.52, but given the number of people you've talked to about this same issue, you believe it is less than 0.52. The hypotheses for this test are Null Hypothesis: p ≥ 0.52, Alternative Hypothesis: p < 0.52. If you randomly sample 29 people and 17 of them believe that global warming is a serious issue, what is your test statistic and p-value?

Question 11 options:

1)

Test Statistic: 0.714, P-Value: 0.238

2)

Test Statistic: -0.714, P-Value: 0.238

3)

Test Statistic: 0.714, P-Value: 1.524

4)

Test Statistic: -0.714, P-Value: 0.762

5)

Test Statistic: 0.714, P-Value: 0.762

In: Statistics and Probability