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Content Check Lessons 6.1??

Last updated over 1 year ago
14 questions
Required
4

From a large group of people who signed a card saying they intended to quit smoking, a random sample of 1000 people was selected. It turned out that 210 (21%) of the sampled individuals had not smoked over the past 6 months.
Match the corresponding terms:

Draggable itemCorresponding Item
The true proportion who had not smoked.
Population
21% had not smoked
Parameter
1000 people that intend to quit smoking
Sample
All people that intend to quit smoking
Statistic
Required
4

A pediatrician wants to know the 75th percentile for the distribution of heights of 10-year-old boys, so she selects a sample of 50 10-year-old male patients and calculates that the 75th percentile in the sample is 56 inches.
Match the corresponding terms:

Draggable itemCorresponding Item
75th percentile
Population
50 10 year old boys
Parameter
All 10 year old boys
Sample
75th percentile = 56 in.
Statistic
Exercises 3-6 refer to the following population of 2 male students and 3 female students, along with their quiz scores:
Abigail 10
Bobby 5
Carlos 10
DeAnna 7
Emily 9
Required
10

Using the quiz scores for the students above:
FIRST: List all 10 possible SRSs of size n = 3 in the show your work area using the text tool 'T', use the first initial for each person instead of their entire name
SECOND: calculate the range of the quiz scores for each sample (max minus min)
THIRD: display the sampling distribution of the sample range on a dotplot. (use the scribble tool, make the color line thick and create dots)

Required
1

A school newspaper article claims that 60% of the students at a large high school completed their assigned homework last week. Some statistics students want to investigate if this claim is true, so they choose an SRS of 100 students from the school to interview.
When they found that only 45 of the 100 students completed their assigned homework last week, they suspected that the proportion of all students who completed their assigned homework last week is less than the 60% claimed by the newspaper.
To determine if a sample proportion of = 0.45 provides convincing evidence that the true proportion is less than p = 0.60, the class simulated 250 SRSs of size n = 100 from a population in which p = 0.60.
Here are the results of the simulation:

There is one dot on the graph at 0.73. Explain what this dot represents.

Required
2

Would it be surprising to get a sample proportion of 0.45 or less in an SRS of size 100 when p = 0.60? Explain.

Required
2

Based on your answer to #5, is there convincing evidence that the proportion of all students who completed their assigned homework last week is less than p = 0.60? Explain.

Exercises 7-11 refer to the following setting. The manager of a grocery store records the total amount spent (in dollars) for each customer who makes a purchase at his store during a week. The values in the table summarize the distribution of amount spent for this population:
Required
2

Is the median unbiased? To investigate if the sample median is an unbiased estimator of the population median, 1000 SRSs of size n = 10 were selected from the population described. The sample median for each of these samples was recorded on the dotplot.
The mean of the simulated sampling distribution is indicated by an orange line segment.

Does the sample median appear to be an unbiased estimator of the population median? Explain your reasoning.

Required
3

What would happen to the sampling distribution of the sample median if the sample size were n = 50 instead? Justify with three answers.
(see the dotplot in #7)

Required
2

Is the minimum unbiased? To investigate if the sample minimum is an unbiased estimator of the population minimum, 1000 SRSs of size n = 10 were selected from the population described. The sample minimum for each of these samples was recorded on the dotplot. The mean of the simulated sampling distribution is indicated by an orange line segment.
Does the sample minimum appear to be an unbiased estimator of the population minimum? Explain your reasoning.

Select both answers.

Required
2

Is the range unbiased? To investigate if the sample range is an unbiased estimator of the population range, 1000 SRSs of size n = 10 were selected from the population described. The sample range for each of these samples was recorded on the dotplot. The mean of the simulated sampling distribution is indicated by an orange line segment.
Does the sample range appear to be an unbiased estimator of the population range?
Explain your reasoning.
Select both answers.

Required
3

What would happen to the sampling distribution of the sample range if the
sample size were n = 5 instead? Justify with three answers.
(see the dotplot in #10)

Information for #12 - 14:
Lefties Eleven percent of students at a large high school are left-handed. A statistics teacher selects a random sample of 100 students and records X = the number of left-handed students in the sample.
Required
1
Use the information above to answer:
Round your answers to two places past the decimal.
  1. p= _______
  2. Calculate the mean of the sampling distribution of X: _______
  3. Calculate the standard deviation of the sampling distribution of X: _______
Required
5

Would it be appropriate to use a normal distribution to model the sampling distribution
of X = the number of left-handed students in the sample? Justify your answer.

Required
2
Calculate the probability that at least 15 of the members of the sample are left-handed.
Use normal distribution calculations to find your answer:
Here are the steps:
z-score for 15: _______ round to two places past the decimal

P(X > 15) = _______ round your answer to four places past the decimal
Hint: you are looking for the area GREATER than or equal to 15, what do you need to do?