Based on a survey of 160 persons employed by the state of North Carolina, the mean and standard deviation of their ages are found to be 36 and 10 years, respectively. Determine a 90% confidence interval for the mean age of the state of North Carolina employees. Round your answer to the nearest integer.

In a pet shelter for cats only, there were 45 black cats, 30 long-haired cats, and 30 cats who were old (> 10 years old). For this study, cats in the shelter were classified as black/not-black, young/old, and long-haired/short-haired. 12 cats were black, young and long-haired, 10 were black, short-haired and old, 5 were black, long-haired and old, and none of the cats were long-haired, non-black and old.

a. How many total cats were in this shelter (i.e., how many cats were black or long-haired or old)?

b. How many cats were black, short-haired, and young?

c. How many cats were long-haired, not-black, and young?

d. How many cats were short-haired, not-black, and old?

Note: Define your events first (cat is black, cat is long-haired, and cat is old), and show your work using equations or Venn diagrams

Assume we flip a fair coin 100 times. Use the normal approximation to the binomial distribution to approximate the probability of getting more than 60 heads.

Answer: 0.0108 - need work

1. According to Stats Canada, 15% of Canadians in 2015 were considered "low income". A researcher believes that number has changed since that time. A large random sample of Canadians is selected to test the researcher's claim.

a. Determine what population parameter is being tested:

i) μ  

ii) p

iii) ρ

b. Determine if the alternative hypothesis is a left-tailed, right-tailed, or two-tailed test:

i) < : left-tailed

ii) > : right-tailed

iii) ≠ : two-tailed

show your work please

In a study of speed dating conducted at Columbia University, 15 female subjects were asked to rate the attractiveness of their male dates, and a sample showed the results to be a mean of 7.35 and standard deviation of 2.70. Construct a 95% confidence interval.

final answer

For all hypothesis tests, you must show the four steps:

1. Hypotheses

2. Test statistic

3. p-value or p-value approximation

4. Conclusion sentence (Do no just say ”Reject the null hypothesis” or ”Fail to reject the

null hypothesis”)

If doing the hypothesis test in jamovi, you must include the jamovi output but show the four

steps separately as well.

Exercises

1. The Department of Natural Resources (DNR) received a complaint from recreational fishermen that

a community was releasing sewage into the river where they fished. These types of releases lower the

level of dissolved oxygen in the river and hence cause damage to the fish residing in the river. An

inspector from the DNR designs a study to investigate the fishermen’s claim. Fifteen water samples

are selected at locations on the river upstream from the community and fifteen samples are selected

downstream from the community. The dissolved oxygen readings in parts per million (ppm) are given

in the following table.

Data available online: Ex 1 Data

Above

5.2

4.8

5.1

5.0

4.9

4.8

5.0

4.7

4.7

5.0

4.7

5.1

5.0

4.9

4.9

Below

4.2

4.4

4.7

4.9

4.6

4.8

4.9

4.6

5.1

4.3

5.5

4.7

4.9

4.8

4.7

(a) Perform a hypothesis test to test whether the mean oxygen levels upstream (above) is unequal to

the mean oxygen content downstream (below). Use α = 0.01. (10 points)

(b) Estimate the size of the difference in the mean dissolved oxygen readings for the two locations on

the river using a 99% confidence interval. Assume σ1does not =σ2 (5 points)

(c) Assuming σ1=σ2, estimate the size of the difference in the mean dissolved oxygen readings for

the two locations on the river using a 99% confidence interval. (5 points)

The research director at the Nie Pójdzie Motor Club was interested whether the annual miles driven by residents of Arkansas was greater than the 2019 average of 13,452 annual miles for a driver in the South Central region. A random sample of licensed Arkansan drivers was drawn, and a hypothesis test was performed using the .05 significance level. Some parts of the output are shown below. Please answer the following questions (a to g) using the output below. (3.5 pts.)

a) What are the degrees of freedom?

b) State the H₀ and H_a.

c) Identify the decision rule using the critical value of t (round to three decimal places).

d) Identify the decision rule using the p value method.

e) State the test statistic (t _calc)

f) What is the p value?

g) Do you reject or not reject H₀? Explain your decision using the output

1. What type of study is this?

2. Based on description of the study, what is (are) the dependent variable(s)?

3. Classify the variable(s) you listed in #2 in each of the three ways.

4. What is (are) the independent variables?

5. Classify the variable(s) you listed in #4 in each of the three ways.

6. List two confounding variables that may offset the conclusions of this experiment.

7. What measures could have been taken in order to control for these confounding variable?

A sock company is considering branching off and manufacturing gloves. In order to determine the types of gloves to make and sell, they randomly selected and interviewed 500 people. In the interview, subject was asked their age and profession. Then they were given four different gloves: leather, cotton, fleece and polyester. After trying each pair on, they were told that they could take and keep whichever pair they preferred.

The researchers concluded that lawyers prefer leather gloves, teachers prefer cotton gloves, and adults between 18 and 30 prefer polyester of fleece gloves.

Consider the following randomly arranged in 3 classes data of a sample.

1. Plot the cumulative histogram and the polygon and interpret. (2.5+2.5+2.5=7.5)
2. Determine the Range (5)
3. Determine the mean and the median. (7.5+7.5=15)
4. Determine the standard deviation. (7.5)
5. Determine the relative frequency and determine the percentage of observation having a value equal or lower than 12. (5+2.5)

The load-bearing capacities (in thousands of pounds) of five transmission line insulators are 64 , 48 , 19, and 79. Use a sample size of 2 to

a). find the mean and standard deviation of the population.

b). list all samples (with replacement) of the given size from the population and find the mean of

      each.

c). Find he mean and standard deviation of the sampling distribution of sample means.

Suppose a developmental psychologist is interested in the effects of fluoride in water on children’s heights. She measures the heights of a random sample (N = 21) of 12-year old children who live in an area with a very high level of natural fluorides in the water. She is interested in comparing the average height of these children with the known population mean height, which she takes from published growth tables (µ = 58.0 inches for 12-year olds). The data file ‘fluoride-spring2020.csv’ gives her raw sample data. Answer the following questions. You will want to take some of your answers from spss.

Spps file data:

. (3 pts) If the sample of 21 children was unbiased, and the sample size was made much larger and remained unbiased, what would you predict about the decision about the null hypothesis in that case? (That is, would you expect to reject the null or fail to reject it?) Explain why or why not.

J. (2 pts) Imagine that the sample size got much larger (as in sub-question h), but that the sample mean and standard deviation remained unchanged. In that case, what would happen to the value of Cohen’s d?

K. (3 pts) Calculate the 95% confidence interval (CI) for estimating the population mean, based on the sample. (Do this by hand; the option to find the CI in JASP is for the difference between the two means, not the estimate of the population mean based on the sample data.)   

L. (2 pts) Describe why it makes sense that the number 58.0 either should or should not be included in the 95% CI, based on your decision about H₀. In other words, how does knowing the CI complement the result from testing the null hypothesis?

A ski company in Vail owns two ski shops, one on the west side and one on the east side of Vail. Ski hat sales data (in dollars) for a random sample of 5 Saturdays during the 2004 season showed the following results. Is there a significant difference in sales dollars of hats between the west side and east side stores at the 10 percent level of significance?

(b) State the decision rule for a 5 percent level of significance. (Round your answers to 3 decimal places.)

Reject the null hypothesis if t_calc < ( ) or t_calc > ( ).

(c-1) Find the test statistic t_calc. (Round your answer to 2 decimal places. A negative value should be indicated by a minus sign.)

t_calc ( )