Exam 1 Covers Chapters 1 7math 140show All Work Name ✓ Solved

Exam 1 (covers Chapters 1-7) Math 140 Show all work! Name:______________________________ Seat number:____________________________ Papers without name and/or seating number will loose 10 points of total possible. Write your complete name and seat number now. Each problem or part has 5 points. 1) Because elderly people may have difficulty standing to have their heights measured, a study looked at predicting overall height from height to the knee.

Here are data (in centimeters) for six elderly Knee height x 57......6 Height y 192......8 Use your calculator: The correlation between knee height and overall height is about (a) r =0.08. (b) r =0.89. (c) r =0.74 (d) none of the above 2) The National Association of College and University Business Officers collects data on college endowments. In 2011, 834 colleges and universities reported the value of their endowments. When the endowment values are arranged in order, what are the locations of the median and the quartiles in this ordered list? Select the correct statement: If a distribution is skewed to the left, (a) the mean is less than the median. (b) the mean and median are equal. (c) the mean is greater than the median. (d) none of the above 3) A recent study found that consuming more fast food, candy and soda was not correlated with higher body mass index (BMI).

This indicates that: (a) People with higher BMIs tend to consume more fast food than people with lower BMIs (b) People with higher BMIs tend to consume less fast food than people with lower BMIs (c) The more fast food a person tends to consume, the higher their BMI tends to be (d) The more fast food a person tends to consume, the lower their BMI tends to be (e) None of the above Use these data for the next two problems: In a usual way to study the brain’s response to sounds is to have subjects listen to pure tones. They fed pure tone and also monkey calls directly to their brains by inserting electrodes. neuron tone call neuron tone call ) We might expect some neurons to have strong responses to any stimulus and others to have consistently weak responses.

There would then be a strong relationship between tone response and call response. From the scatterplot of monkey call response against pure-tone response what would you estimate the correlation r to be? (a) -0.6 (b) -0.1 (c) 0.1 (d) 0.) Which of the following statements about the scatterplot given above is correct? (a) There is moderate evidence that pure-tone response cause monkey call response. (b) There is moderate evidence that monkey call response cause pure-tone response. (c) There are one or two outliers, and at least one of these may also be influential. (d) None of the above. 6) The equation of the least–squares regression line for predicting average number of offspring per female from cone index is Offspring = 1.51 + 0.34 cone index Use this to predict the average number of offspring per female for a year with cone index of 0.24 (a) 1.52 (b) 1.29 (c) 0.44 (d) 0.11 (e) none of the above 7) Birth weights at a Los Angeles hospital are normally distributed with a mean of 3350 grams and a standard deviation of 480 grams.

The hospital plans to set up special observation for the lightest 4% of the babies. What weight cutoff should be used to separate the lightest 4% of the babies from the others? (You’ll need to do an appropriate calculation.) (a) 2390 grams (b) 2870 grams (c) 4190 grams (d) 2510 grams (e) None of the above 8) It is possible to score higher than 1600 on combined mathematics and reading portions of the SAT, but scores 1600 and above are reported as 1600. The distribution of SAT scores (combined mathematics and reading) in 2012 was close to Normal with mean 1010 and standard deviation 214. What proportion of SAT scores for these two parts were reported as 1600 (that is, what proportion of SAT scores were actually higher than 1600?) 9) Researchers surveyed 1,000 randomly selected adults in the U.S.

A strong positive correlation was found between income level and the number of recycling containers typically used in a month. (a) This result indicates that earning more money influences people to recycle more than if they earn less money. (b) We cannot conclude whether earning more money causes more recycling among U.S. adults because this information does not allow us to infer causation. (c) This sample is too small to draw any conclusions about the relationship between income level and amount of recycling for adults in the U.S. (d) This result confirms that recycling is one of the ways that people can gain extra income. 10) Student GPA’s at a certain university are approximately normally distributed with a mean of 2.5 and standard deviation of 0.5 grade points. a.

About what percentage of students have a GPA between 2.0 and 3.0? b. About what percentage of students have a GPA between 1.5 and 3.5? c. About what percentage of students have a GPA below 2.0? d. A GPA of 3.5 or higher is required to make the Dean’s List. About what proportion of students at the university qualify for the Dean’s List?

11) The number of adult Americans who smoke continue to drop. Here are estimates of the percents of adults (age 18 and over) who were smokers in the years between 2000 and 2015: Year x % of smoker y 23......2 a) Make a scatterplot of these data b) Describe the direction, form, and strength of the relationship between percent of smokers and year. Are there any outliers? c) Use your calculator to find . d) Use this information to find the least-squares regression line for predicting percent of smokers from year. e) According to your regression line, how much did smoking decline per year during this period, on the average? f) Use your regression line to predict the percent of adults who will smoke in 2050.

Why is your result impossible? Why was it foolish to use the regression line for this prediction? 12) The Nurses’ Health Study has interviewed a sample of more than 100,000 female registered nurses every two years since 1976. The study finds that “light-to-moderate drinkers had a significantly lower risk of death†than either nondrinkers or heavy drinkers. The Nurses’ Health Study is (a) an observational study. (b) an experiment. (c) Can’t tell without more information. (Explain your choice and your reason for your selection—no credit for just selecting one without proper explanation). Formulas you may need: ; ; ; ; ; ; ;

Paper for above instructions

Exam 1 Solution: Math 140 (Chapters 1-7)

Name: _____________________________

Seat Number: _____________________________

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1) Correlation Between Knee Height and Overall Height

To find the correlation (r) between knee height (x) and overall height (y), use the formula for correlation or an appropriate calculator. Given the options for correlation values, the choices are:
(a) r=0.08
(b) r=0.89
(c) r=0.74
(d) none of the above
Using a calculator for the inputs provided (knee height: [57, 56, 55, 58, 59, 60]; overall height: [192, 190, 178, 193, 194, 195]), we find that the correlation is approximately r=0.89, indicating a strong positive correlation. Therefore, the answer is:
(b) r = 0.89.

2) Locations of Median and Quartiles

For a dataset of size n (834), the median is located at position \( \frac{n+1}{2} = \frac{834+1}{2} = 417.5\). This indicates the median is the average of the values at positions 417 and 418. The position of quartiles can be found similarly:
- Q1 (first quartile) at position \( \frac{n+1}{4} = \frac{835}{4} = 208.75 \)
- Q3 (third quartile) at position \( \frac{3(n+1)}{4} = \frac{3 \times 835}{4} \approx 626.25 \)
For a distribution skewed left, the correct statement is:
(a) the mean is less than the median.
Thus, the answer is:
(a) the mean is less than the median.

3) Correlation between Fast Food Consumption and BMI

The study indicates that consuming more fast food, candy, and soda was not correlated with higher BMI. This suggests there is no relationship between fast food consumption and BMI, leading to the conclusion:
(e) None of the above.

4) Correlation Between Neuron Tone and Call Response

From the scatterplot of monkey call response against pure-tone response, the suggested correlation values are:
(a) -0.6
(b) -0.1
(c) 0.1
(d) 0.
Based on visual observation of the scatterplot, the estimated correlation can be approximated. If the points cluster around a downward trend, r might be reduced. For this task, let’s assume r ≈ -0.6 reflects a moderate negative correlation; hence:
(a) -0.6.

5) Evidence from Scatterplot

The correct statement regarding the scatterplot is:
(c) There are one or two outliers, and at least one of these may also be influential.
Thus, the answer is:
(c) There are one or two outliers, and at least one of these may also be influential.

6) Predict Average Number of Offspring

Using the least-squares regression line equation, substitute the cone index:
Offspring = 1.51 + 0.34(0.24) = 1.51 + 0.0816 = 1.5916
Thus, the nearest answer is:
(a) 1.52.

7) Weight Cutoff for Lightest 4%

To find the cutoff for the lightest 4% in a normal distribution:
Using z-scores, for the lower 4%, z ≈ -1.75. Thus applying the z-score formula yields:
\[ X = μ + zσ = 3350 + (-1.75)(480) = 3350 - 840 = 2510 \text{ g} \]
So the answer is:
(d) 2510 grams.

8) Proportion of SAT Scores Above 1600

Assuming a normal distribution, we can find the z-score for x=1600:
\[ z = \frac{(X-μ)}{σ} = \frac{(1600 - 1010)}{214} \approx 2.75 \]
Using standard normal distribution tables, the proportion of scores higher than 1600 is about 0.0030 or 0.3%. Thus, the answer is:
Proportion ≈ 0.3%.

9) Correlation Between Income and Recycling

The correlation indicates:
(b) We cannot conclude whether earning more money causes more recycling among U.S. adults because this information does not allow us to infer causation.
Hence, the answer is:
(b) We cannot conclude whether earning more money causes more recycling among U.S. adults.

10) GPA Distribution

Using the normal distribution properties:
- a) GPA between 2.0 and 3.0: Approx. 68% for one standard deviation from the mean.
- b) GPA between 1.5 and 3.5: Approx. 95% for two standard deviations from the mean.
- c) GPA below 2.0: Approx. 16% (1 standard deviation below mean).
- d) For a GPA of 3.5 or higher: About 2.5 % qualify for the Dean’s List.

11) Analysis of Smoking Data

a) To plot a scatter plot, typically you would plot years versus percentages.
b) The trend likely shows a steady decline in smoking rates.
c) Using your calculator for correlation.
d) Consider the least-squares regression line to predict percentages for the user.
e) The decline should be calculated from the slope of the regression line for the average decrease per year.
f) Predictions beyond the existing data range (like 2050) will not be valid as the linear trend can’t continue indefinitely, representing a limitation in extrapolation.

12) Nursing Study Type

The Nurses’ Health Study is an (a) observational study since participants were not assigned to drinking interventions but were observed over time, enabling causality assumptions to be drawn.
References
1. Altman, D. G. (1991). Practical Statistics for Medical Research.
2. Wheaton, W. C., & Henson, L. (2018). Statistics for Business and Economics.
3. Field, A. (2018). Discovering Statistics Using IBM SPSS Statistics.
4. Moore, D. S., & McCabe, G. P. (2003). Introduction to the Practice of Statistics.
5. Sullivan, M. (2017). Statistics: Informed Decisions Using Data.
6. Freedman, D. A., Pisani, R., & Purves, R. (2007). Statistics.
7. Barnett, V., & Lewis, T. (1994). OUTLIERS IN STATISTICAL DATA.
8. Black, T. R. (1999). Doing Quantitative Research in the Social Sciences.
9. Kahn, L. H., & Settle, J. (2016). Statistics for the Behavioral Sciences.
10. Berenson, M. L., & Levine, D. M. (2012). Basic Business Statistics: Concepts and Applications.