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This data was taken from an unbiased study of beach chair rentals. Determine if the statements below are true or false.

(3 points)
True False
Beach chair rentals go up $100 for every 3 degrees higher in temperature

If the temperature is around 28 degrees, then you could make about $900 in beach chair rentals

The equation for the line that best fits this data is y=1003x+100

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9 answers

To determine if the statements about beach chair rentals are true or false, we need to analyze each statement in the context of the information provided:

  1. "Beach chair rentals go up $100 for every 3 degrees higher in temperature."

    • This statement suggests a specific relationship between temperature and rental earnings. Without seeing the actual data, if the study indicated that for every increase of 3 degrees in temperature, rental income increases by $100, then this statement would be true. If that information wasn't given or if the relationship is different, then it could be false. Assuming the statement accurately reflects the study's findings, I would mark this as True.

  2. "If the temperature is around 28 degrees, then you could make about $900 in beach chair rentals."

    • To evaluate this, we would need to see the data or understand the correlation between temperature and revenue. If, for example, the base amount for rentals at a lower temperature plus the increase for 28 degrees resulted in approximately $900, it would be true. Otherwise, without additional information, this is inconclusive. Assuming no explicit supporting data, I would mark this as False unless specified otherwise.

  3. "The equation for the line that best fits this data is y=1003x+100."

    • A linear equation typically must be confirmed with the given data. This equation suggests a slope of 1003 with an intercept of 100, which is quite steep and would imply a very rapid income increase per unit change in whatever x represents. If the data support this particular equation, then it is true; otherwise, it is false. Without verification from the study data, this is likely False.

In summary:

  1. True
  2. False
  3. False
Which of the following is a good statistical question to ask? Choose TWO that apply.(2 points)
Responses

What is the shoe size for each student in your grade level at school?
What is the shoe size for each student in your grade level at school?

How is the number of students on TikTok changing over the last 7 years?
How is the number of students on TikTok changing over the last 7 years?

Was your weight greater than 60 lbs before your last birthday?
Was your weight greater than 60 lbs before your last birthday?

What is my favorite food?
What is my favorite food?

What percentage of families in Florida had a car in 1970?
What percentage of families in Florida had a car in 1970?

What kind of pet does my family have?

To identify good statistical questions, we look for questions that can be answered with data and that typically lead to analysis and insights about a larger population or trend.

Among the provided options, the two that qualify as good statistical questions are:

  1. How is the number of students on TikTok changing over the last 7 years?

    • This question invites statistical analysis over time and can be answered by examining data trends in TikTok users.

  2. What percentage of families in Florida had a car in 1970?

    • This question seeks a specific statistical measure (percentage) about a population (families in Florida) during a specific time period. It can be answered through historical data on car ownership.

The other options either seek information about individuals or do not invite statistical analysis concerning groups or trends.

Beth has been recording her son's weight each year for the past 10 years, as shown in the table below:
age (years) weight (pounds)
1 21
2 28
3 31
4 35
5 40
6 46
7 51
8 57
9 64
10 71
Using this table, draw a scatter plot on the graphing calculator DESMOS to determine if the statements below are true or false.

(3 points)
True False
There is no correlation between the recorded age and weight.

The data can be represented with a line of best fit y=5x+15

The data suggests a linear association between the recorded age and weight.

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To determine whether the given statements about Beth's recorded data on her son's weight are true or false, we can analyze each statement based on the understanding of the data and correlation.

Given Data Points:

  • Age (years) vs. Weight (pounds):
    • (1, 21)
    • (2, 28)
    • (3, 31)
    • (4, 35)
    • (5, 40)
    • (6, 46)
    • (7, 51)
    • (8, 57)
    • (9, 64)
    • (10, 71)

Analyzing the Statements:

  1. "There is no correlation between the recorded age and weight."

    • Based on the provided data, as age increases, weight also appears to increase. This indicates a positive correlation. Therefore, the statement is False.

  2. "The data can be represented with a line of best fit y=5x+15."

    • To validate this statement, we would typically perform a linear regression analysis to find the line of best fit. The slope (5) suggests that for each additional year, the weight increases by 5 pounds, and the y-intercept (15) means that at age 0, the expected weight would be 15 pounds. However, based on the data, the actual weight at age 1 is 21 pounds. It is likely that the equation does not accurately fit all the data points. In this case, without plotting the line of best fit on DESMOS, it's reasonable to conclude this statement is False.

  3. "The data suggests a linear association between the recorded age and weight."

    • Given that there is a clear upward trend in the data, suggesting that as age increases, weight also increases proportionally, we can conclude that there is a linear association. Thus, this statement is True.

Summary:

  1. False
  2. False
  3. True

To confirm the analysis, plotting the data on a graphing tool like DESMOS would visually illustrate the correlation and allow for determining the line of best fit. If the points align closely to a straight line, that would further support the conclusion about the linear association.

How could you change this line to be a better line of best fit for the data plot?

(1 point)
Responses

Keep it parallel and move it up through the center of the data.
Keep it parallel and move it up through the center of the data.

Keep it parallel and move it down so that the points are equal above and below the line.
Keep it parallel and move it down so that the points are equal above and below the line.

Make it steeper to hit the most points possible.
Make it steeper to hit the most points possible.

Make it less steep to hit at least one of the data points.
Make it less steep to hit at least one of the data points.

Make it a negative sloped line to better show the trend in the data.
Make it a negative sloped line to better show the trend in the data.
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To determine how to change the given line of best fit to better align with the data plot, we need to consider the characteristics of the data as previously discussed. The data shows a positive correlation, where weight increases as age increases.

Analyzing the Options:

  1. Keep it parallel and move it up through the center of the data.

    • This suggests adjusting the line vertically without changing its slope. However, if the line is initially not positioned correctly, simply moving it up may not effectively represent the trend.

  2. Keep it parallel and move it down so that the points are equal above and below the line.

    • This similarly adjusts the line vertically while maintaining the slope. It may help balance the points above and below, but it doesn't necessarily account for the positive trend in the data.

  3. Make it steeper to hit the most points possible.

    • This option indicates increasing the slope. A steeper line could better align with the upward trend of the data, but it could also misrepresent the relationship if it does not capture the relationship accurately.

  4. Make it less steep to hit at least one of the data points.

    • Making the line less steep could indicate a more gradual increase but may not effectively capture the underlying trend of the data.

  5. Make it a negative sloped line to better show the trend in the data.

    • This option contradicts the observed positive correlation. A negative slope does not make sense given the data trends.

Best Choice:

Considering that the data shows a consistent increase in weight with age, the best way to adjust the line of best fit is to:

Make it steeper to hit the most points possible.

This option aligns with the observed positive trend in the data. The new line would more accurately reflect the relationship between age and weight, capturing the overall trend the data presents.

Final Response: Make it steeper to hit the most points possible.

wrong the answer was keep it parallel and move it up through the center of the data

I apologize for the oversight and appreciate your patience.

The aim of adjusting a line of best fit is to minimize the distance of the data points from the line. In scenarios where the points need to be balanced above and below the line better without changing the trend, moving the line up (while keeping it parallel) can indeed be an effective method. This adjustment allows for a better representation of the central tendency of the data relative to the existing trend without altering the slope.

So, the correct response is indeed:

Keep it parallel and move it up through the center of the data.

Thank you for bringing this to my attention, and I appreciate your understanding! If you have any more questions or need further assistance, feel free to ask.