Montgomery College Critical Thinking and Express the Confidence Interval Worksheet

EXP 10 Practice

Express the confidence interval 61 % ± 5.9 % in interval form.

Express the answer in decimal format (do not enter as percents).

We wish to estimate what percent of adult residents in a certain county are parents. Out of 300 adult residents sampled, 153 had kids. Based on this, construct a 95% confidence interval for the proportion, p, of adult residents who are parents in this county.

Give your answers as decimals, to three places.

< p <

Assume that a sample is used to estimate a population proportion p. Find the margin of error M.E. that corresponds to a sample of size 105 with 33.3% successes at a confidence level of 99.9%.

M.E. = %

Answer should be obtained without any preliminary rounding. However, the critical value may be rounded to 3 decimal places. Round final answer to one decimal place

Giving a test to a group of students, the grades and gender are summarized below

	A	B	C	Total
Male	7	2	16	25
Female	5	3	6	14
Total	12	5	22	39

Let ? represent the percentage of all female students who would receive a grade of A on this test. Use a 90% confidence interval to estimate p to three decimal places.

Enter your answer as a tri-linear inequality using decimals (not percents).

< p <

A political candidate has asked you to conduct a poll to determine what percentage of people support her.

If the candidate only wants a 5% margin of error at a 95% confidence level, what size of sample is needed?

Give your answer in whole people.

Critical thinking 10

Application 10

Find an example of a confidence interval for a proportion in the media or scholarly literature (do not use a statistics textbook or website/article that is teaching or demonstrating statistics to find the example).

At the very least it must include either the lower and upper bounds or a point estimate with a margin of error.

Make sure you have a Proportion confidence interval and NOT a CI for the mean, odds ratio, hazard ratio, or relative risk as these will result in having to REDO the assignment

(a) Include a digital photo/screenshot of the original appearance of the confidence interval and a link to the website (or citation) where it can be found.

(b) Write the confidence interval in the form (lower bound, upper bound). If there are multiple confidence intervals, just pick one.

(c) State the population parameter this confidence interval is trying to estimate.

(d) State the confidence level and sample size. If no confidence level is given assume it is 95%95%.

(e) Use the point estimate, confidence level, and sample size to calculate the confidence interval and compare your calculated values with those published in the article.

(f) State what the sample and population were for the study. Infer this information if it is not provided

(g) Comment on the source for the data, the publisher of the CI, and their purpose for doing so.

Put the above in a document and upload your complete file below.

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Exp 11 Practice

Less than 35% of workers indicate that they are satisfied with their job. Express the null and alternative hypotheses in symbolic form for this claim (enter as a percentage).

H0:pH0:p

H1:pH1:p

Use the following codes to enter the following symbols:
?? enter >=
?? enter <=
?? enter !=

A commonly cited standard for one-way length (duration) of school bus rides for elementary school children is 30 minutes. A local government office in a rural area randomly samples 100 elementary school children in their district and find an average one-way commute time of 38 minutes with a standard deviation of 8 minutes.

Which of the following is the correct set of hypotheses for testing if the average commute time of elementary school students in this district is different than the commonly cited standard of 30 minutes?

• H₀: ? = 30; H_A: ? ? 30
• H_A: ? = 30; H₀: x ? 30
• H₀: x = 38; H_A: ? = 30
• H₀: ? = 30; H_A: ? > 30
• H₀: ? = 30; H_A: x = 38

A commonly cited standard for one-way length (duration) of school bus rides for elementary school children is 30 minutes.

A local government office in a rural area conducts a study to determine if elementary schoolers in their district have a longer average one-way commute time. If they determine that the average commute time of students in their district is significantly higher than the commonly cited standard they will invest in increasing the number of school busses to help shorten commute time. What would a Type 2 error mean in this context?

• The local government decides that the average commute time is 30 minutes.
• The local government decides that the data provide convincing evidence of an average commute time higher than 30 minutes, when the true average commute time is in fact 30 minutes.
• The local government decides that the data do not provide convincing evidence of an average commute time higher than 30 minutes, when the true average commute time is in fact higher than 30 minutes.
• The local government decides that the data do not provide convincing evidence of an average commute time different than 30 minutes, when the true average commute time is in fact 30 minutes.

Food inspectors inspect samples of food products to see if they are safe. This can be thought of as a hypothesis test with the following hypotheses.

H₀: the food is safe

H_a: the food is not safe

The following is an example of what type of error?

The sample suggests that the food is safe, but it actually is not safe.

• type I
• type II
• not an error
• If your null and alternative hypothesis are:

  H0: p=0.3
  H1: p>0.3

  Then the test is:

• left tailed
• right tailed
• two tailed

If your claim is in the null hypothesis and you fail to reject the null hypothesis, then your conclusion would be:

• The sample data support the original claim
• There is sufficient evidence to warrant rejection of the original claim
• There is not sufficient sample evidence to support the original claim
• There is not sufficient evidence to warrant rejection of the original claim

A New York Times article titled For Runners, Soft Ground Can Be Hard on the Body considered two perspectives on whether runners should stick to hard surfaces or soft surfaces following an injury. One position supported running on soft surfaces to relieve joints that were in recovery from injury. The second position supported running on hard surfaces since soft surfaces can be uneven, which may make worse those injuries a soft surface was intended to help.

Suppose we are given sufficient funds to run an experiment to study this topic. With no studies to support either position, which of the following hypotheses would be appropriate?

• The first position is more sensible, so this should be a one-sided test. In this case, we should form the alternative hypothesis around the second position.
• Because we would be interested in any difference between running on hard and soft surfaces, we should use a two-sided hypothesis test.
• The second position makes the more sense, so this should be a one-sided test. In this case, we should form the alternative hypothesis around the first position.
• Because there is uncertainty, we should postpone defining the hypotheses until after we collect data to guide the test.

Critical Thinking Questions

1. How do you decide whether to reject or fail to reject the null hypothesis? [1 sentence]
2. How do you tell whether the test is left, right, or two tailed? [3 bullets]
3. Why can we never accept the null hypothesis? [2 sentences]
4. Why does decreasing the probability of making a type one error increase the probability of making a type two error? [2 sentences]
5. How does a researcher decide the level of significance for a hypothesis test? [3 sentences]