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. Determine 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
Natural sampling variation is the only reason that Tyson appears to have a higher proportion of packages with bacterial contamination.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. 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 inferenceone-sample inference twice
Question 6. Why don't the results agree? 2 submission only; no exceptions
Tyson chicken is sold in less sanitary supermarkets.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.The one- and two-sample procedures for analyzing the data are equivalent; the results differ in this problem only because of natural sampling variation.
Question 1:
For Tyson packages,
n = 75
x = 35
Sample proportion:
(Round to 4 decimal)
Confidence level = c = 0.90
z critical value for (1+c)/2 = (1+0.90)/2 = 0.95 is
zc = 1.645 (From statistical table of z values, average of 1.64 and 1.65, (1.64+1.65)/2 = 1.645)
90% confidence intervals for the proportion of Tyson packages with contamination is
(Round to 3 decimal)
90% confidence intervals for the proportion of Tyson packages with contamination is (0.372, 0.561)
Lower Bound = 0.372
Upper Bound = 0.561
For Perdue packages
n = 75
x = 22
Sample proportion:
(Round to 4 decimal)
Confidence level = c = 0.90
z critical value for (1+c)/2 = (1+0.90)/2 = 0.95 is
zc = 1.645 (From statistical table of z values, average of 1.64 and 1.65, (1.64+1.65)/2 = 1.645)
90% confidence intervals for the proportion of Perdue packages with contamination is
(Round to 3 decimal)
90% confidence intervals for the proportion of Perdue packages with contamination is (0.207, 0.380)
Lower Bound = 0.207
Upper Bound = 0.380
In a recent issue of Consumer Reports, Consumers Union reported on their investigation of bacterial contamination...
Recent incidents of food contamination have caused great concern
among consumers. An article reported that 33 of 80 randomly
selected Brand A brand chickens tested positively for either
campylobacter or salmonella (or both), the leading bacterial causes
of food-borne disease, whereas 69 of 80 Brand B brand chickens
tested positive.
(a)
Does it appear that the true proportion of non-contaminated
Brand A chickens differs from that for Brand B? Carry out a test of
hypotheses using a significance level 0.01....
We will use this prompt for this and the next 1 question. A survey reported in Time magazine included the question ‘‘Do you favor a federal law requiring a 15 day waiting period to purchase a gun?” Results from a random sample of US citizens showed that 318 of the 520 men who were surveyed supported this proposed law while 379 of the 460 women sampled said ‘‘yes”. Use this information to find a 90% confidence interval for the difference...
In 2003, an organization surveyed 1,508 adult Americans and asked about a certain war, "Do you believe the United States made the right or wrong decision to use military force?" Of the 1,508 adult Americans surveyed, 1,080 stated the United States made the right decision. In 2008, the organization asked the same question of 1,508 adult Americans and found that 573 believed the United States made the right decision. Construct and interpret a 90% confidence interval for the difference between...
In 2003, an organization surveyed 1,500 adult Americans and asked about a certain war, "Do you believe the United States made the right or wrong decision to use military force?" of the 1,500 adult Americans surveyed, 1,080 stated the United States made the right decision in 2008, the organization asked the same question of 1,500 adult Americans and found that 580 believed the United States made the right decision Construct and interpreta 90% confidence interval for the difference between the...
In 2003, an organization surveyed 1,500 adult Americans and
asked about a certain war, "Do you believe the United States made
the right or wrong decision to use military force?" Of the 1,500
adult Americans surveyed, 1,080 stated the United States made the
right decision. In 2008, the organization asked the same question
of 1,500 adult Americans and found that 575 believed the United
States made the right decision. Construct and interpret a 90%
confidence interval for the difference between...
In 2003, an organization surveyed 1 comma 510 adult Americans and asked about a certain war, "Do you believe the United States made the right or wrong decision to use military force?" Of the 1 comma 510 adult Americans surveyed, 1 comma 086 stated the United States made the right decision. In 2008, the organization asked the same question of 1 comma 510 adult Americans and found that 573 believed the United States made the right decision. Construct and interpret...
Score: 0 of 1 pt 10 of 10 (6 complete)> HW Score: 43.33%, 4.33 of 10 pts Instructor-created question Question Help n 2003, an organization surveyed 1,500 adult Americans and asked about a certain war, "Do you believe the United States made the right or wrong decision to use military force?" Of the 1,500 adult Americans surveyed, 1,090 stated the United States made the right decision. In 2008, the organization asked the same question of 1,500 adult Americans and found...
1, In 1943, an organization surveyed 1100 adults and asked, "Are you a total abstainer from, or do you on occasion consume, alcoholic beverages?" Of the 1100 adults surveyed, 385 indicated that they were total abstainers. In a recent survey, the same question was asked of 1100 adults and 363 indicated that they were total abstainers. Complete parts (a) and (b) below. (a) Determine the sample proportion for each sample. The proportions of the adults who took the 1943 survey...
When is unknown and the sample is of size n 230, there are two methods for computing confidence intervals for u. (Notice that, When is unknown and the sample is of size n<30, there is only one method for constructing a confidence interval for the mean by using the student's t distribution with d.f. = n - 1.) Method 1: Use the Student's t distribution with d.f. = n - 1. This is the method used in the text. It...
A study considered the question, 'Are you a registered voter?" Accuracy of response was confirmed by a check of city voting records. Two methods of survey were used: a face-to-face interview and a telephone interview. A random sample of 85 people were asked the voter registration question face to face. Of those sampled, seventy-six respondents gave accurate answers (as verified by city records). Another random sample of 90 people were asked the same question during a telephone interview. Of those...