A 2^3 design is confounded in 4 blocks of size 2. The principal block contains treatments (1) and abc. Another block contains a. What is the second element of that block. (b, c, ab, ac, or bc?)

A research group conducted an extensive survey of 2942 wage and salaried workers on issues ranging from relationships with their bosses to household chores. The data were gathered through hour-long telephone interviews with a nationally representative sample. In response to the question, "What does success mean to you?" 1562 responded, "Personal satisfaction from doing a good job." Let p be the population proportion of all wage and salaried workers who would respond the same way to the stated question. Find a 90% confidence interval for p. (Round your answers to three decimal places.)

Two Sample Hypothesis Test

Show all five steps in your analysis. To get full credit you must label the CV (critical value) and TV (Test Value) in your drawing. Use the p-value for this test.

A teacher claims that students retain more when reading a novel than when watching a movie version of the novel. Each student read a novel and watched a film version of a different novel. Then they were given a test on both the novel and the movie. A researcher randomly selected a sample of 8 students. Using a one sample statistical test on their differences, test the results at an alpha level of .05. The results are shown in the table below:

What type of test are you going to perform? ______________________________

Overproduction of uric acid in the body can be an indication of cell breakdown. This may be an advance indication of illness such as gout, leukemia, or lymphoma.† Over a period of months, an adult male patient has taken eleven blood tests for uric acid. The mean concentration was x = 5.35 mg/dl. The distribution of uric acid in healthy adult males can be assumed to be normal, with σ = 1.79 mg/dl.

(a) Find a 95% confidence interval for the population mean concentration of uric acid in this patient's blood. What is the margin of error? (Round your answers to two decimal places.)

(b) What conditions are necessary for your calculations? (Select all that apply.)

σ is knownnormal distribution of uric acidσ is unknownn is largeuniform distribution of uric acid

(c) Interpret your results in the context of this problem.

The probability that this interval contains the true average uric acid level for this patient is 0.95.We are 5% confident that the true uric acid level for this patient falls within this interval.     The probability that this interval contains the true average uric acid level for this patient is 0.05.We are 95% confident that the true uric acid level for this patient falls within this interval.

(d) Find the sample size necessary for a 95% confidence level with maximal margin of error E = 1.04 for the mean concentration of uric acid in this patient's blood. (Round your answer up to the nearest whole number.)
blood tests

Foot Locker uses sales per square foot as a measure of store productivity. Last year, the mean annual sales per square foot was $410 with a standard deviation of $54.38. Suppose you take a random sample of 36 Foot Locker stores operating last year. There is a 3% probability that the sample mean annual sales per square foot is at most $______.

A researcher wishes to estimate the proportion of adults who have high-speed internet access. What size sample should be obtained if she wishes the estimate to be within 0.01 with 90% confidence if...

a. She uses a previous estimate of 0.42? N=

b. She does not use any prior estimates? N=

Read each problem carefully and clearly show all work.

Indicate calculator functions used (ie T-Test, 2-SampTTest, etc) as well as calculator entries

State your conclusions in terms of the context of the problem.

1. Does the time of day that a class meets affect exam grades? Exam grades for an 8am statistics class and a 3pm statistics class taught by the same professor were compared. The summary data are given in the table below. Assuming both populations are approximately normally distributed, is there a difference between the two classes? Use a significance level of 5%.

      Clearly label the 6 step approach

1. Following the UK referendum in 2016, 910 randomly sampled UK voters were asked which of the following options they agreed most with (i) the UK should negotiate an exit deal with the EU, then have a second referendum, (ii) the UK should negotiate an exit deal with the EU then enact Article 50, or (iii) the UK should enact Article 50 immediately. The results of the survey by political ideology are shown below.

Po/itico/ ideology

1. What percent of these voters identify themselves as labour?
2. What percent of these voters are in favour of enacting Article 50immediately?
3. What percent of the voters who identify themselves as Conservatives are also in favour of the “negotiate then referendum” option? What percent of Labour share this view? What percent of Liberal share this view? [Compute 3 conditional probabilities.]
4. Do political ideology and views on Article 50 appear to be independent? No formal testing is required, but make sure to explain your reasoning.

Phenomenology or case study? Ethnography or historical? Content analysis or grounded theory? Which research design (and why) would be best to use for a qualitative study on school culture and teacher turnover?

3. The Mathematics & Statistics department at Lancaster University claims that, on average, 25% of students obtain a first class degree. A competitor university is interested in showing that this value is an overestimate. They randomly sample 82 graduates and find that 18 have a host class degree

1. What are the assumptions for conducting a hypothesis test around this data? Are these satisfied?
2. What is your null hypothesis?
3. What is your alternative hypothesis?
4. Calculate the p-value for the hypotheses you proposed in (b) &(c).
5. What is your conclusion when conducting a 95% hypothesis test?
6. Do you agree with the competitor university that the proportion of first-class degrees advertised is an overestimate? State your reasoning.

Questions 18 – 28. A researcher is interested in whether psychology students are less happy than other students. The mean happiness score for the population is 8. The researcher administers a happiness scale to 25 BC students and obtains a mean of 5 and variance of 49.The researcher uses an alpha level of 0.05.

18. Is this a one- or two-tailed test?

19. What is the null hypothesis?

20. What is the alternative hypothesis?

21. What are the degrees of freedom?

22. What is t critical?

23. What is the standard error?

24. What is the t statistic (t obtained)?

25. What decision would you make about H0?

26. What can you conclude?

27. What is the effect size?

28. What does this effect size mean?

A bank wants to evaluate which credit card would be more attractive to its customers, one with a high interest rate for unpaid balances but no annual fee or one with a low interest rate for unpaid balances for an annual fee of $50. Foe a random sample of 100 of its 52,000 customers, 40 said they prefer the one that has an annual fee. Would you conclude statistically that more people prefer the card with no annual fee?

Test the hypothesis that customers are more likely to prefer the card with no annual fee than if they were randomly selecting for the significance level of 0.05.

An elevator has a placard stating that the maximum capacity is

16201620

lblong dash—1010

passengers.​ So,

1010

adult male passengers can have a mean weight of up to

1620 divided by 10 equals 162 pounds.1620/10=162 pounds.

If the elevator is loaded with

1010

adult male​ passengers, find the probability that it is overloaded because they have a mean weight greater than

162162

lb.​ (Assume that weights of males are normally distributed with a mean of

171 lb171 lb

and a standard deviation of

26 lb26 lb​.)

Does this elevator appear to be​ safe?An elevator has a placard stating that the maximum capacity is

16201620

lblong dash—1010

passengers.​ So,

1010

adult male passengers can have a mean weight of up to

1620 divided by 10 equals 162 pounds.1620/10=162 pounds.

If the elevator is loaded with

1010

adult male​ passengers, find the probability that it is overloaded because they have a mean weight greater than

162162

lb.​ (Assume that weights of males are normally distributed with a mean of

171 lb171 lb

and a standard deviation of

26 lb26 lb​.)

Does this elevator appear to be​ safe?

When σ is unknown and the sample is of size n ≥ 30, there are two methods for computing confidence intervals for μ. (Notice that, When σ 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 is widely employed in statistical studies. Also, most statistical software packages use this method.

Method 2: When n ≥ 30, use the sample standard deviation s as an estimate for σ, and then use the standard normal distribution.
This method is based on the fact that for large samples, s is a fairly good approximation for σ. Also, for large n, the critical values for the Student's t distribution approach those of the standard normal distribution.

Consider a random sample of size n = 30, with sample mean x = 45.2 and sample standard deviation s = 5.3.

(a) Compute 90%, 95%, and 99% confidence intervals for μ using Method 1 with a Student's t distribution. Round endpoints to two digits after the decimal.

(b) Compute 90%, 95%, and 99% confidence intervals for μ using Method 2 with the standard normal distribution. Use s as an estimate for σ. Round endpoints to two digits after the decimal.

(c) Compare intervals for the two methods. Would you say that confidence intervals using a Student's t distribution are more conservative in the sense that they tend to be longer than intervals based on the standard normal distribution?

No. The respective intervals based on the t distribution are shorter.

Yes. The respective intervals based on the t distribution are shorter.  

Yes. The respective intervals based on the t distribution are longer.

No. The respective intervals based on the t distribution are longer.

(d) Now consider a sample size of 50. Compute 90%, 95%, and 99% confidence intervals for μ using Method 1 with a Student's t distribution. Round endpoints to two digits after the decimal.

(e) Compute 90%, 95%, and 99% confidence intervals for μ using Method 2 with the standard normal distribution. Use s as an estimate for σ. Round endpoints to two digits after the decimal.

(f) Compare intervals for the two methods. Would you say that confidence intervals using a Student's t distribution are more conservative in the sense that they tend to be longer than intervals based on the standard normal distribution?

Yes. The respective intervals based on the t distribution are longer.

Yes. The respective intervals based on the t distribution are shorter.   

No. The respective intervals based on the t distribution are longer.

No. The respective intervals based on the t distribution are shorter.

With increased sample size, do the two methods give respective confidence intervals that are more similar?

As the sample size increases, the difference between the two methods remains constant.As the sample size increases, the difference between the two methods is less pronounced.    As the sample size increases, the difference between the two methods becomes greater.

Suppose that a consumer advocacy group would like to conduct a survey to find the proportion p of smartphone users that were happy with their smartphone. The advocacy group took a random sample of 1,000 smartphone users and found that 400 were happy with their smartphone. A 90% confidence interval for p is closest to: