Abbie wants to determine whether handedness affects scores on the Picture Arrangement subtest of the WAIS III, as this test is suggested to tap right-brain processing powers.  Abbie gives the test to a group of right-handers and a group of left-handers; their scores are below:

Left-handed:  12, 10, 12, 14, 12, 10, 8                Right-handed: 8, 10, 10, 12, 11, 6, 7, 5, 9, 8

Test Abbie’s hypothesis that left-handed participants have superior Picture Arrangement scores compared to right-handers; with an alpha of .01.

a. State the H₀ and H₁ hypotheses, in statistical notation, and identify the critical t value(s).

b. Calculate standard error and the observed t-statistic.  What is your decision regarding the null hypothesis?  Why?

c. State your results in nonstatistical terms.

Figure 1 shows the schematic diagram of a mechanical system that consists of two subsystems in parallel. The first subsystem consists of two components A and B in series, both of which have the same 0.80 probability of working. The second subsystem consists of three components C, D, and E in series, all of which have the same 0.90 probability of working. It is assumed that all components of the system are independent. (a) What is the probability that subsystem A-B works? (5 points) (b) What is the probability that subsystem C-D-E works? (5 points) (c) What is the probability that the whole system works? Hint: Remember that the probability that the system works = 1 – probability that the system doesn’t work. (7 points) (d) What is the probability that A is not working, given that the system works? Hint: Does it matter whether B works or not? (8 points)

Calculate a 95 percent confidence interval for the proportion of interest. Make sure you check all conditions. (high interval) 0.397 and (low interval) 0.257 How do you do the success-failure condition for number 5? (when checking to see if all conditions are met).

3. The Pew Research Center conducted a survey in 2019 asking U.S. adults about their experiences dating online. In a random sample of 200 adults aged 18-49, 114 said dating sites are a safe way to meet people. In a random sample of 200 adults aged 50+, 82 said dating sites are a safe way to meet people. Research question: Are U.S. adults aged 18-49 more likely to say dating sites are safe than those aged 50+?

a. What are the hypothesis statements to answer the research question?

b. Are the appropriate conditions met to conduct a hypothesis test using the standard normal distribution? Explain.

c. Compute the value of the test statistic.

d. Find p-value using the appropriate theoretical distribution in StatKey (include screenshot from StatKey): p-value =

e. What is your conclusion in the context of this study?

Trevor is interested in purchasing the local hardware/electronic goods store in a small town in South Ohio. After examining accounting records for the past several years, he found that the store has been grossing over $850 per day about 60% of the business days it is open. Estimate the probability that the store will gross over $850

1. at least 6 out of 10 business days.

0.68256

2. at most 3 of the 10 business days.

3. fewer than 7 out of 20 business days.

4. more than 16 out of 20 business days.

5. What is the expected (mean) number of business days for which the store would gross over $850 in a month (30 days)?

A USA based cable broadband company wants to compare the average customer satisfaction scores between its east coast and west coast customer bases. The customer survey asks for a score between 1 and 5, with 1 being poor and 5 being excellent.
174 east coast customers are surveyed, and the sample mean is 3.51 with a sample standard deviation of 0.51. For the west coast, 355 customers are surveyed, and the sample mean is 3.24 with a sample standard deviation of 0.52.

a. Create a 95% confidence interval for the average score for west coast customers. Interpret this interval in context of the problem.

b. Now say you consider the difference between the average scores between west coast and east coast. Create a 95% confidence interval for the difference in average scores (specify what difference you are considering).

c. The company wants to investigate if the average score of the east coast customers is higher than the average score of the west coast customers. Write the null and alternative to test this hypothesis.

d. Compute the test statistic for this problem and describe how you would obtain the p-value for this test.

e. Say the p-value is very close to 0. In a sentence or two explain what that means in context of this problem.

assume that s and t are independent exponentially distributed, set u = min(s,t), v = max(s,t). prove that u and w = v-u are independent

The reading speed of second grade students in a large city is approximately​ normal, with a mean of 91 words per minute​ (wpm) and a standard deviation of 10 wpm.

Complete parts​ (a)

What is the probability that a random sample of 26 second grade students from the city results in a mean reading rate of more than 95 words per​ minute? The probability is _________ ​(Round to four decimal places as​ needed.)

Friendly Cabinet Makers is a company that builds cabinets for houses. The company recently employed a new building technique that is supposed to save time over the old method which had a mean of 6.5 hours. Friendly Cabinet Makers wants to determine if the new method actually saves time. A random sample was taken of number of hours to build a cabinet. At the .05 significance level, can Friendly Cabinet Makers conclude that the new method is faster? Using the data in the range A10:A59, run a hypothesis test and make a concluding statement..

Can someone please answer this question? thank you

You think that, in addition to cannabis use, road conditions may also affect driving abilities and contribute to an increased risk of road accidents. You suggest that further testing be made using 5 different road-condition scenarios in the virtual driving simulator. Your proposal is accepted and a new group of 60 individuals are solicited to participate in the study and are randomly assigned to one of the various treatment groups.

1. [6 marks] Test the following hypothesis at the 1% significance level; make sure you follow all the steps for hypothesis testing indicated in the Instructions section and show your computations.
   1. Significant interaction effect between cannabis intake and road conditions;
   2. Significant main effect of the cannabis intake factor (if warranted);
   3. Significant main effect of the road conditions factor (if warranted).

Here we are going to test a couple of hypotheses about the Old Faithful data in R. Remember, this is the faithful data frame that is built in to R. You can use data(faithful) to load data set. First split faithful into two separate data frames: (1) those entries with eruption times less than 3 minutes (eruptions < 3) and (2) those entries with eruption times greater than or equal to 3 minutes (eruptions >= 3). Answer the following about the entry wait time (waiting):

(a) For the entries with short eruption times, you want to test the hypothesis that the associated waiting last on average less than 60 minutes. What is the null hypothesis? What is the alternative hypothesis? (Write your own code) (10 pt)

(b) Give R commands to compute the statistic that you used in (a) and the resulting p-value. What values did you get? Would you reject the null hypothesis at the α = 0.05 level? (15 pt)

(c) For the entries with long eruption times, you want to test the hypothesis that the associated waiting time last on average shorter than 80 minutes. What is the null hypothesis? What is the alternative hypothesis? (Write your own code) (10 pt)

(d) Give R commands to compute the statistic you used in (c) and the resulting p-value to test the hypothesis you came up with in part (c). What values did you get? Would you reject the null hypothesis at the α = 0.05 level? (15 pt)

Suppose that the minimum and maximum ages for typical textbooks currently used in college courses are 00 and 88 years. Use the range rule of thumb to estimate the standard deviation.
Standard deviation =  Find the size of the sample required to estimage the mean age of textbooks currently used in college courses. Assume that you want 9292% confidence that the sample mean is within 0.250.25 year of the population mean. Required sample size =

In a study conducted to investigate browsing activity by shoppers, each shopper was initially classified as a nonbrowser, light browser, or heavy browser. For each shopper, the study obtained a measure to determine how comfortable the shopper was in a store. Higher scores indicated greater comfort. Suppose the following data were collected.

a. Use a=.05 to test for a difference among mean comfort scores for the three types of browsers.

Compute the values identified below (to 2 decimals, if necessary).

Calculate the value of the test statistic (to 2 decimals, if necessary).

The p-value is - Select your answer -less than .01between .01 and .025between .025 and .05between .05 and .10greater than .10Item 6

What is your conclusion?

- Select your answer -Conclude that the mean comfort scores are not all the same for the browser groupsDo not reject the assumption that the mean comfort scores are equal for the browser groupsItem 7

b. Use Fisher's LSD procedure to compare the comfort levels of nonbrowsers and light browsers. Use a=.05.

Compute the LSD critical value (to 2 decimals).

What is your conclusion?

The candy Reese's Pieces comes in three different colors: orange, yellow, and brown. The target color distribution is 45% of the pieces orange. 27.5% yellow, and 27.5% brown. A random sample of Reese's Pieces packages contained 400 pieces having the following color distribution: 162 were orange, 117 yellow, and 121 brown.

Test the hypothesis that Reese's Pieces is meeting its target color distribution. Use α = .01 (define the population parameter(s) in H₀). (Which hypothesis is your claim)

1. H₀:
2. H_a:
3. T. S.:
4. R (Draw Rejection region with the critical value)
5. Conclusion:

Based on your test of hypothesis, which statement would you agree with (choose one)?

__________ Reese's Pieces is probably meeting its target color distribution.

__________ Reese's Pieces is probably not meeting its target color distribution.

6. Approximate the p-value for your test statistic in part a) using the χ²

7. Suppose the maximum value of α that you are willing to tolerate is .10. What would be your conclusion?

Another way to obtain a p-value is through computer simulation. Use the statistical program StatKeyto obtain a p-value for your test statistic in part a) (see directions).

You obtain this frequency distribution that displays a sample of scores from the population; calculate standard deviation for this sample. Round answer to two decimal places.