Question

Moose Drool Makes Grass More Appetizing Different species can interact in interesting ways. One type of grass produces the toxin ergovaline at levels about 1.0 part per million in order to keep grazing animals away. However, a recent study27 has found that the saliva from a moose counteracts these toxins and makes the grass more appetizing (for the moose). Scientists estimate that, after treatment with moose drool, mean level of the toxin ergovaline (in ppm) on the grass is 0.183. The standard error for this estimate is 0.016.
Give notation for the quantity being estimated, and define any parameters used.

Give notation for the quantity that gives the best estimate, and give its value.

Give a 95% confidence interval for the quantity being estimated. Interpret the interval in context.

3.68 Bisphenol A in Your Soup Cans Bisphenol A (BPA) is in the lining of most canned goods, and recent studies have shown a positive association between BPA exposure and behavior and health problems. How much does canned soup consumption increase urinary BPA concentration? That was the question addressed in a recent study34 in which consumption of canned soup over five days was associated with a more than 1000% increase in urinary BPA. In the study, 75 participants ate either canned soup or fresh soup for lunch for five days. On the fifth day, urinary BPA levels were measured. After a two-day break, the participants switched groups and repeated the process. The difference in BPA levels between the two treatments was measured for each participant. The study reports that a 95% confidence interval for the difference in means (canned minus fresh) is 19.6 to 25.5 μg/L.

Is this a randomized comparative experiment or a matched pairs experiment? Why might this type of experiment have been used?

What parameter are we estimating?

Interpret the confidence interval in terms of BPA concentrations.

If the study had included 500 participants instead of 75, would you expect the confidence interval to be wider or narrower?

3.70 Effect of Overeating for One Month: Average Long-Term Weight Gain Overeating for just four weeks can increase fat mass and weight over two years later, a Swedish study shows.35 Researchers recruited 18 healthy and normal-weight people with an average age of 26. For a four-week period, participants increased calorie intake by 70% (mostly by eating fast food) and limited daily activity to a maximum of 5000 steps per day (considered sedentary). Not surprisingly, weight and body fat of the participants went up significantly during the study and then decreased after the study ended. Participants are believed to have returned to the diet and lifestyle they had before the experiment. However, two and a half years after the experiment, the mean weight gain for participants was 6.8 lbs with a standard error of 1.2 lbs. A control group that did not binge had no change in weight.

What is the relevant parameter?

How could we find the actual exact value of the parameter?

Give a 95% confidence interval for the parameter and interpret it.

Give the margin of error and interpret it.

Answer 1

Answer:

Step-by-step explanation:

Hello!

1)

The variable of interest is

X: level of toxin ergovaline on the grass after being treated with Moose saliva.

>The parameter of interest is the population mean of the level of ergovaline on grass after being treated with Moose saliva: μ

The best point estimate for the population mean is the sample mean:

>X[bar]=0.183 Sample average level of ergovaline on the grass after being treated with Moose saliva.

Assuming that the sample comes from a normal population.

>There is no information about the sample size takes to study the effects of the Moose saliva in the grass. Let's say that they worked with a sample of n=20

Using the Student-t you can calculate the CI as:

X[bar] ± $t_{n-1;1-\alpha /2}$ * $\frac{S}{\sqrt{n} }$

Where   $t_{n-1;1-\alpha /2}= t_{19;0.975}= 2.093$

0.183 ± 2.093 * (0.016/√20)

[0.175;0.190]

Using a 95% confidence level you'd expect that the interval [0.175;0.190] will contain the true average of ergovaline level of grass after being treated with Moose saliva.

2)

The information of a study that shows how much does the consumption of canned soup increase urinary BPA concentration is:

Consumption of canned soup for over 5 days increases the urinary BPA more than 1000%

75 individuals consumed soup for five days (either canned or fresh)

The study reports that a 95% confidence interval for the difference in means (canned minus fresh) is 19.6 to 25.5 μg/L.

>This experiment is a randomized comparative experiment.

Out of the 75 participants, some randomly eat canned soup and some randomly eaten fresh soup conforming to two separate and independent groups that were later compared.

>The parameter of interest is the difference between the population mean of urinary BPA concentration of people who ate canned soup for more than 5 days and the population mean of urinary BPA concentration of people that ate fresh soup for more than 5 days.

>Using a 95% confidence level you'd expect that the interval 19.6 to 25.5 μg/L would contain the value of the difference between the population mean of urinary BPA concentration of people who ate canned soup for more than 5 days and the population mean of urinary BPA concentration of people that ate fresh soup for more than 5 days.

> If the sample had been larger, then you'd expect a narrower CI, the relationship between the amplitude of the CI and sample size is indirect. Meaning that the larger the sample, the more accurate the estimation per CI is.

3)

> The parameter of interest is Average Long-Term Weight Gain Overeating for just four weeks can increase fat mass and weight over two years later of people with an average age of 26 years old.

> The only way of finding the true value of the parameter is if you were to use the information of the whole population of interest, this is making all swedes with an average age of 26 increase calorie intake by 70% (mostly by eating fast food) and limit their daily activity to a maximum of 5000 steps per day and then measure their weight gain over two years. since this es virtually impossible to do, due to expenses and size of the population, is that the estimation with a small but representative sample is conducted.

>

n= 18

X[bar]= 6.8 lbs

S= 1.2

X[bar] ± $t_{n-1;1-\alpha /2}$ * (S/√n)

6.8 ± 2.101 * (1.2/√18)

$t_{n-1;1-\alpha /2}= t_{17;0.975}= 2.101$

[6.206;7.394]

With a 95% confidence level, you'd expect that the interval [6.206;7.394] will contain the true value of the Average Long-Term Weight Gain Overeating for just four weeks can increase fat mass and weight over two years later of people with an average age of 26 years old.

>

The margin of error of the interval is

$t_{n-1;1-\alpha /2}$ * (S/√n)= 2.101 * (1.2/√18)= 0.59

With a 95% it is expected that the true value of the Average Long-Term Weight Gain Overeating for just four weeks can increase fat mass and weight over two years later of people with an average age of 26 years old. will be 0.59lbs away from the sample mean.

I hope it helps