The price of a gallon of milk at 16 randomly selected Arizona
stores is given below. Assume that milk prices are normally
distributed. At the α=0.10α=0.10 level of significance, is there
enough evidence to conclude that the mean price of a gallon of milk
in Arizona is less than $3.00? (Round your results to three
decimal places)
Which would be correct hypotheses for this test?
Gallon of Milk prices:
| 2.85 | 3.23 | 3.23 | 2.93 |
| 3.07 | 2.75 | 3.17 | 2.51 |
| 2.89 | 3.23 | 2.79 | 2.77 |
| 2.61 | 3.17 | 2.85 | 2.75 |
test statistic:
Give the P-value:
In: Math
If X is a normal random variable with parameters σ2 = 36 and μ =
10, compute (a) P{X ≥ 5} .
(b) P{X = 5}.
(c) P{10>X≥5}.
(d) P{X < 5}.
(e) Find the y such that P{X > y} = 0.1.
In: Math
For a standard normal distribution, what is the probability that z is greater than 1.65
In: Math
In a recent issue of Consumer Reports, Consumers Union reported on their investigation of bacterial contamination in packages of name brand chicken sold in supermarkets. Packages of Tyson and Perdue chicken were purchased. Laboratory tests found campylobacter contamination in 35 of the 75 Tyson packages and 22 of the 75 Perdue packages.
Question 1. Find 90% confidence intervals for the proportion of Tyson packages with contamination and the proportion of Perdue packages with contamination (use 3 decimal places in your answers).
_____ lower bound of Tyson interval
_____ upper bound of Tyson interval
_____ lower bound of Perdue interval
_____ upper bound of Perdue interval
Question 2. The confidence intervals in question 1 overlap. What does this suggest about the difference in the proportion of Tyson and Perdue packages that have bacterial contamination? One submission only; no exceptions
The overlap suggests that there is no significant difference in the proportions of packages of Tyson and Perdue chicken with bacterial contamination.
Even though there is overlap, Tyson's sample proportion is higher than Perdue's so clearly Tyson has the greater true proportion of contaminated chicken.
Question 3. Find the 90% confidence interval for the difference in the proportions of Tyson and Perdue chicken packages that have bacterial contamination (use 3 decimal places in your answers).
_____ lower bound of confidence interval
_____ upper bound of confidence interval
Question 4. What does this interval suggest about the difference in the proportions of Tyson and Perdue chicken packages with bacterial contamination? One submission only; no exceptions
We are 90% confident that the interval in question 3 captures the true difference in proportions, so it appears that Tyson chicken has a greater proportion of packages with bacterial contamination than Perdue chicken.
Natural sampling variation is the only reason that Tyson appears to have a higher proportion of packages with bacterial contamination.
Tyson's sample proportion is higher than Perdue's so clearly Tyson has the greater true proportion of contaminated chicken.
Question 5. The results in questions 2 and 4 seem contradictory. Which method is correct: doing two-sample inference, or doing one-sample inference twice? One submission only; no exceptions
two-sample inference
one-sample inference twice
Question 6. Why don't the results agree? 2 submission only; no exceptions
The one- and two-sample procedures for analyzing the data are equivalent; the results differ in this problem only because of natural sampling variation.
If you attempt to use two confidence intervals to assess a difference between proportions, you are adding standard deviations. But it's the variances that add, not the standard deviations. The two-sample difference-of-proportions procedure takes this into account.
Different methods were used in the two samples to detect bacterial contamination.
Tyson chicken is sold in less sanitary supermarkets.
In: Math
Which of the following variables yields data that would be suitable for use in a histogram? __________
|
the time concentrating on a math problem |
||
|
color of hair |
||
|
brand of TV |
||
|
gender of a student |
In: Math
Problem 6: Researchers are testing two new cholesterol medications. Medication is given to some males and females and a placebo is given to others. The tablesbelow summarize the resulting HDL cholesterol levels after 8 weeks.
Problem 6a: Is there evidence of effect modification with medication A? Provide a brief (1-2 sentences) explanation.
| Medication A | |||
| Women | N | Mean HDL | Std Dev of HDL |
| New drug | 40 | 35.47 | 2.45 |
| Placebo | 41 | 38.42 | 3.42 |
| Men | N | Mean HDL | Std Dev of HDL |
| New drug | 10 | 46.19 | 1.35 |
| Placebo | 9 | 39.06 | 2.89 |
Problem 6b: Is there evidence of effect modification with medication B? Provide a brief (1-2 sentences) explanation.
| Medication B | |||
| Women | N | Mean HDL | Std Dev of HDL |
| New drug | 40 | 46.12 | 2.19 |
| Placebo | 41 | 39.24 | 2.47 |
| Men | N | Mean HDL | Std Dev of HDL |
| New drug | 10 | 45.25 | 1.89 |
| Placebo | 9 | 39.06 | 2.22 |
In: Math
The ages of a group of 135 randomly selected adult females have a standard deviation of 17.9 years. Assume that the ages of female statistics students have less variation than ages of females in the general population, so let sigmaequals17.9 years for the sample size calculation. How many female statistics student ages must be obtained in order to estimate the mean age of all female statistics students? Assume that we want 95% confidence that the sample mean is within one-half year of the population mean. Does it seem reasonable to assume that the ages of female statistics students have less variation than ages of females in the general population?
In: Math
1. A consumer group is testing camp stoves. To test the heating capacity of a stove, they measure the time required to bring 2 quarts of water from 50 degrees to boiling.
Two competing models are under consideration. Thirty-six stoves of each model were tested and the following results were obtained.
Model 1: mean time is 11.4 and standard deviation is2.5
Model 2: mean time is 9.9 and standard deviation is 3.0
In: Math
2. a. Use signifcance test to test the indicated claim. A standard aptitude test is given to several randomly selected programmers, and the scores are given below for the mathematics and verbal portions of the test. At the 0.05 level of significance, test the claim that programmers do better on the mathematics portion of the test.
Mathematics 447 540 427 456 527 449 477 498 425
Verbal 385 478 343 371 440 371 394 422 385
b. Find a 90% confidence interval for the difference of the mean.
In: Math
What criteria would you look at when conducting a statistical analysis to determine which online dating site(s) someone should use, and why? If you would not consider online dating for yourself, ask a friend who has been or is participating in online dating for their input. For example, do you think it is necessary to simply fill in the answers in the profile, such as height, body type, hair color, etc., and your preferences in these same categories for your match? Or do you think it is also necessary to answer the questions that can help find someone who may be more suited to your personality? These types of questions cover a variety of genres, such as relationships, sex, politics and law, and life and death.4 You can also find information online about statistics indicating which site yields the most success. Success may be determined by the site that yields the most number of dates, or the most marriages. In your response, share with your peers what success determinate you found or looked for. What sample size do you think you would need to determine which site is most likely to yield the greatest success? In your response, please provide a link to an article about dating sites or a link to dating site that explains what kind of data these sites provide.
In: Math
A study found that the mean amount of time cars spent in drive-throughs of a certain fast-food restaurant was
157.6157.6
seconds. Assuming drive-through times are normally distributed with a standard deviation of
3434
seconds, complete parts (a) through (d) below.Click here to view the standard normal distribution table (page 1).
LOADING...
Click here to view the standard normal distribution table (page 2).
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(a) What is the probability that a randomly selected car will get through the restaurant's drive-through in less than
118118
seconds?The probability that a randomly selected car will get through the restaurant's drive-through in less than
118118
seconds is
nothing.
(Round to four decimal places as needed.)
(b) What is the probability that a randomly selected car will spend more than
210210
seconds in the restaurant's drive-through?The probability that a randomly selected car will spend more than
210210
seconds in the restaurant's drive-through is
nothing.
(Round to four decimal places as needed.)
(c) What proportion of cars spend between
22
and
33
minutes in the restaurant's drive-through?The proportion of cars that spend between
22
and
33
minutes in the restaurant's drive-through is
nothing.
(Round to four decimal places as needed.)
(d) Would it be unusual for a car to spend more than
33
minutes in the restaurant's drive-through? Why?
In: Math
Many studies have suggested that there is a link between exercise and healthy bones. Exercise stresses the bones and this causes them to get stronger. One study examined the effect of jumping on the bone density of growing rats. There were three treatments: a control with no jumping, a low-jump condition (the jump height was 30 centimeters), and a high-jump condition (60 centimeters). After 8 weeks of 10 jumps per day, 5 days per week, the bone density of the rats (expressed in mg/cm3 ) was measured. Here are the data. data190.dat
(a) Make a table giving the sample size, mean, and standard deviation for each group of rats. Consider whether or not it is reasonable to pool the variances. (Round your answers for x, s, and s_(x^^\_) to one decimal place.)
Group n x^^\_ s s_(x^^\_)
Control
Low jump
High jump
(b) Run the analysis of variance. Report the F statistic with its degrees of freedom and P-value. What do you conclude? (Round your test statistic to two decimal places and your P-value to three decimal places.)
F =
P =
Conclusion: There is statistically no/a significant difference between the three treatment means at the α = .05 level.
obs group g density 1 Control 1 616 2 Control 1 613 3 Control 1 609 4 Control 1 619 5 Control 1 664 6 Control 1 602 7 Control 1 571 8 Control 1 585 9 Control 1 600 10 Control 1 609 11 Lowjump 2 623 12 Lowjump 2 620 13 Lowjump 2 622 14 Lowjump 2 653 15 Lowjump 2 622 16 Lowjump 2 634 17 Lowjump 2 647 18 Lowjump 2 636 19 Lowjump 2 642 20 Lowjump 2 660 21 Highjump 3 639 22 Highjump 3 611 23 Highjump 3 586 24 Highjump 3 622 25 Highjump 3 610 26 Highjump 3 605 27 Highjump 3 626 28 Highjump 3 630 29 Highjump 3 605 30 Highjump 3 640
In: Math
According to the National Eye Institute, 8% of men are red-green colorblind. A sample of 125 men is gathered from a particular subpopulation, and 13 men in this sample are colorblind.(Without using z-value)
a. Is this statistically significant evidence that the proportion of red-green colorblind men is greater than the subpopulation than the national average with alpha = 0.05?
b. What is the maximum number of men that could have been colorblind in this sample that would lead you to fail to reject the null hypothesis?
c. Using 8% as the probability of being colorblind, find a 95% confidence interval for the number of men in a sample of 125 who are colorblind.
In: Math
What other examples can you think of where most people have more or less than the average? This is true of most things with a non-symmetric distribution (e.g., weight, math scores, marathon times) but it is nice to continue the theme of the video in terms of risk (e.g., most have below average risk of a automobile accident, death by violence, or even, say, getting a date).
In: Math
The percent of persons (ages five and older) in each state who
speak a language at home other than English is approximately
exponentially distributed with a mean of 8.76.
The lambda of this distribution is
The probability that the percent is larger than 3.24 is P(x ≥ 3.24) =
The probability that the percent is less than 9.79 is P(x ≤ 9.79) =
The probability that the percent is between 5.76 and 11.76 is P(5.76 ≤ x ≤ 11.76) =
In: Math