Iconic memory is a type of memory that holds visual information for about half a second (0.5 seconds). To demonstrate this type of memory, participants were shown three rows of four letters for 50 milliseconds. They were then asked to recall as many letters as possible, with a 0-, 0.5-, or 1.0-second delay before responding. Researchers hypothesized that longer delays would result in poorer recall. The number of letters correctly recalled is given in the table.

(a) Complete the F-table. (Round your values for MS and F to two decimal places.)

(b) Compute Tukey's HSD post hoc test and interpret the results. (Assume alpha equal to 0.05. Round your answer to two decimal places.)

The critical value is  for each pairwise comparison.

State the null and alternative hypotheses for each conjecture.

a. A researcher thinks that if expectant mother use vitamin pills, the birth weight of the babies will increase. The average birth weight of the population is 8.6 pounds.

b. An engineer hypothesizes that the mean number of defects can be decreased in a manufacturing process of compact disks ny using robots instead of humans for certain tasks. The mean number of defective disks per 1000 is 8.

c. A psychologist feels that playing soft music during a test will change the results of the test. The psychologist is not sure whether the grades will be higher or lower. In the past, the mean of the scores was 73.

Suppose we are comparing the mean driving distance between 2 types of golf balls. At the same location, the same golfer drives ball A 40 times and ball B 40 times. For the ball A sample there is a mean of 242 yards with a standard deviation of 41 yards. For the ball B sample there is a mean of 265 yards with a standard deviation of 48 yards.   Does the data show that there is a difference in the mean distance between the two balls? Do a hypothesis test showing all steps to make your conclusion.

A researcher at the Nie Pójdzie Motor Club is interested in the average repair bill for automobile owners when the “check engine” light comes on. He believes that automobiles manufactured overseas (Import) will have lower repair costs (in dollars) than automobiles manufactured in the United States (Domestic). A random sample from each type of manufacturer was drawn.   

The Data Analysis output for the various tests used when comparing two group means are shown below. The significance level was .05.   Identify which two sample test should be performed from the scenario and from the following outputs. Then, answer the questions (a to f) using the correct t test output. (3.5 pts.)

a) What is the appropriate two sample test to perform – the paired t test, the t test assuming equal variances, or the t test assuming unequal variances – for this research project?

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) Do you reject or not reject Ho? Explain your decision.

To see if basketball players improve or get worse as they age we take a random sample of players who compete at both the age of 25 and the age of 30 and find their scoring average for the season at those ages with the results below. Use a hypothesis test to determine if there is evidence that there is a difference in mean points scored between the two ages. Use a significance level of 0.05.

Player                          1          2          3          4          5          6          7                     

Age 25 average           21.3     15.2     7.8       8.2       11.8     17.3     4.6

Age 30 average           19.2     12.8     9.2       6.4       7.4       14.2     2.1

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.

A study was conducted for the effects of marijuana use on college students. Memory recall was evaluated by asking students to sort items.

At the 5% LOS, do the data suggest test that light users correctly sort more items than heavy users?

What is logit model? How it can be responses for multicategory responses?

Suppose a coin is weighted so the probability of heads is really 0.6. Find the exact sampling distribution of the sample proportion of 3 flips of the coin that are heads.

Load “Lock5Data” into your R console. Load “OlympicMarathon” data set in
“Lock5Data”. This data set contains population of all times to finish the 2008
Olympic Men’s Marathon.
a) What is the population size?
b) Now using “Minutes” column generate a random sample of size 5.
c) Calculate the sample mean and record it (create a excel sheet or write a
direct R program to record this)
d) Continue steps (b) and (c) 10,000 time (that mean you have recorded 10,000
sample means)
What you have in step (d) is closely resemble to distribution of sample means
with sample size 5.
e) Calculate the mean of 10,000 sample means.
f) Calculate the population mean (that mean using all data in “Minutes” column)
g) According to the central limit theorem, if conditions satisfied, then the mean of
distribution of sample mean should be close to the population mean. Now
compare your results for part (e) and (f). Are they same or at least close to
each other?
h) Calculate the standard deviation for 10,000 data points you have from above.
i) Now calculate theoretical standard error using the formula !
√! . Here ? is the
standard deviation using all “Minutes” data and ? is the sample size (which is
equal to 5 in this case)

j) Comment about your results in part (h) and (i)
k) Graph your 10,000 records in a histogram
l) Is your histogram close to a normal distribution shape?
m) According to the central limit theorem, if sample size is large enough then
distribution of sample means is close to normal distribution. Let increase the
sample size to see whether this is true or not. Use sample size 40 and repeat
steps (b), (c) and (d) again. Create a histogram for this new data set. Is your
histogram shape look like normal distribution?

In a random sample of ten cars, the mean minor repair cost was $150.00 and the standard deviation was $25.75. If the repair cost is assumed to be normally distributed, construct a 99% confidence interval for the population mean. Give your answer using two decimal digits:

1-the left end of the interval, LCL, is? ...

2- the right end of the interval, UCL, is?...

1.A researcher collects a sample of 30 individuals who have a mean age of 34.6, a median age of 41.5, and a modal age of 44. Make one observation regarding the nature of the distribution of data that the researcher collected.  What would be the best measure of central tendency to use in describing a distribution of this form?  Whydid you choose the measure of central tendency that you did?

2.A statistician computes a 95% confidence interval for the number of prior arrests of those convicted of violent crimes. The interval ranged from 1.6 to 3.6 prior arrests.  Given these data, what is the probability that the population mean is greater than 3.6 prior arrests?  Why?

An article in Fortune magazine reported on the rapid rise of fees and expenses charged by mutual funds. Assuming that stock fund expenses and municipal bond fund expenses are each approximately normally distributed, suppose a random sample of 12 stock funds gives a mean annual expense of 1.50 percent with a standard deviation of 0.38 percent, and an independent random sample of 12 municipal bond funds gives a mean annual expense of 0.73 percent with a standard deviation of 0.40 percent. Let µ₁ be the mean annual expense for stock funds, and let µ₂ be the mean annual expense for municipal bond funds. Do parts a, b, and c by using the equal variances procedure.

(a) Set up the null and alternative hypotheses needed to attempt to establish that the mean annual expense for stock funds is larger than the mean annual expense for municipal bond funds. Test these hypotheses at the 0.05 level of significance. (Round your s_p² answer to 4 decimal places and t-value to 2 decimal places.)

(b) Set up the null and alternative hypotheses needed to attempt to establish that the mean annual expense for stock funds exceeds the mean annual expense for municipal bond funds by more than 0.5 percent. Test these hypotheses at the 0.05 level of significance. (Round your t-value to 2 decimal places and other answers to 1 decimal place.)

(c) Calculate a 95 percent confidence interval for the difference between the mean annual expenses for stock funds and municipal bond funds. Can we be 95 percent confident that the mean annual expense for stock funds exceeds that for municipal bond funds by more than .5 percent? (Round your answers to 3 decimal places.)

rev: 04_03_2020_QC_CS-206802

5. Suppose that researchers study a sample of 50 people and find that 10 are left-handed. (a) Find a 95% confidence interval for the population proportion that is left-handed.

(b) What would the confidence interval be if the researchers used the Wilson value p ̃ instead?

(c) Suppose that an investigator tests the null hypothesis that the population proportion is 18% against the alternative that it is less than that. If α = 0.05 then find the critical value pˆc. Using pˆ as the sample estimate, would the investigator reject the null?

(d) Suppose that researchers are using this critical value but, unbeknownst to them, the true, population proportion is 0.16. Find the power of the test.

a. Tom designed a complete factorial experiment with 2 factors. One factor had 4 levels, the other had 5 levels. For each combination of levels of factors, there were 6 replicates. In the ANOVA table associated with this design, what were the degrees of freedom of the interaction?

a. 7, b. 12,   c. 20, d. 24, e. 30.

b. In the above ANOVA table of the complete factorial experiment, suppose we want to test the significance of the main effect of the factor with 4 levels. What is the distribution we use to calculate p-values?              

a. F(3, 100), b. F (4, 120),    c. F (4, 100), d. F (5, 100), e. F (5, 120).