Scores on the Wechsler Adult Intelligence Scale- Third Edition (WAIS-III) are nationally standardized to be normally distributed with a mean of 100 and standard deviation of 15. A psychologist has a dataset containing the WAIS-III scores from a random sample of 50 adults who are members of a specific organization. They want to know if there is evidence that the mean WAIS-III score in the population of all members of this organization is greater than the known national mean of 100. In the sample of 50 adults, the observed sample mean was 105. When doing any hand calculations, show all work.

1) Our comparison distribution will be a distribution of sample means. What are the shape, mean, and standard deviation (i.e., standard error) of that distribution of sample means?

Q4) The following yields were recorded by using two agricultural products.

Perform a two sample hypothesis test to consider if the yields for product A and product B are different. Use the default significance level of α=0.05.

You may assume that the population variances for product A and B are equal.

You should take the mean of Yield A first in your test statistic.

1. State the Null and Alternative hypotheses.

2. Calculate the test-statistic.    (state accurate to 2dp)

3. State the Degrees of Freedom.

(1 Mark)

4. Look up the upper-tail critical value from tables.

(1 Mark)

5. State your decision regarding H_o.

Q5) 184 patients with coronavirus have been hospitalised in the city hospital. 92 have been treated with anti-viral medication and 92 have not.  

Perform a hypothesis test to determine if there is an association between patients being given anti-viral drugs and developing pneumonia. Use a 5% level of significance.

The Observed frequencies are presented in the table below.

1. Calculate the four expected values under the condition of the Null hypothesis.

2. Calculate the two missing χ² contributions to the test-statistic.

                                                                                       (state accurate to 4dp)

3. Calculate the test statistic, χ²  (state accurate to 2dp).

(1 mark)

4. Look up the critical value from tables and state its value.

(1 mark)

5. State your decision to reject or not reject H_o and confirm or deny whether there is a relationship between drug treatment and pneumonia.

Q6) A sample of the various prices for a particular product has been conducted in 16 stores which were selected at random in a city. The following prices were noted, in GBP:

95, 108, 97, 112, 99, 106, 105, 100, 99, 98, 104, 110, 107, 111, 103, 110.

1. Calculate a 95% confidence interval to estimate the actual mean price of the product in the city. State the interval accurate to 1 decimal place.                                                                                                

2. Is it reasonable to assume that the average price for this product is £100? State your reasoning.                                                                                                                      

3. What size sample would need to be taken to estimate the population mean price within 1 pound?                                                                                                                    

Does a statistics course improve a student's mathematics skills,as measured by a national test? Suppose a random sample of 13 students takes the same national mathematics exam prior to enrolling in a stats course and just after completing the course. At a 1% level of significance determine whether the scores after the stats course are significantly higher than the scores before. Take the differences = before - after.

Before    After
430        465
485        475
520        535
360        410
440        425
500        505
425        450
470        480
515        520
430        430
450        460
495        500
540        530

Locate student 9 in the dataset. What rank will be given to this student? ________.


What is the value of the test statistic, T? Give answer to 1 decimal place. ________.


What is the critical value for the study? (Hint: student 10 will be dropped from the analysis, since the scores are the same before and after the stats class). ________.

Many fast-food restaurants have soft drink dispensers with preset amounts, so that when the operator merely pushes a button for the desired rink the cup is automatically filled. This method apparently saves time and seems to increase worker productivity. A researcher randomly selects 9 workers from a restaurant with automatic dispensers and 9 works from a restaurant with manual dispensers. At a 1% significance level, use the Mann-Whitney U Test to test whether workers with automatic dispensers are significantly more productive.

Automatic (Group 1): 153, 128, 143, 110, 152, 168, 144, 137, 118
Manual (Group 2): 105, 118, 129, 114, 125, 117, 106, 92, 126

What rank will be given to the observation value, 118 that is in both the automatic and manual groups? (Round answer to 1 decimal). ___________.


When rounding the U test statistic up to the next value, what is the p-value from the Mann Whitney Table of p-values? (Round to 4 decimal places) ___________.

Consider the following sample:

120, 94, 88, 67, 82, 106, 140, 102, 87, 99, 106, 86, 105, 93

a) Calculate the sample mean and the sample standard deviation

b) Calculate the sample range. What does it mean?

c) What is the mode of the data distribution?

d) Construct a box plot and interpret the result.

e) Identify the 45th percentile and interpret the result.

f) If the two largest data from above data distribution is removed, then what will be its impact on the result that you have obtained in (a)?

A sample size of 56 with x=62.2 and s=18.1 is used to estimate a population mean mu.Find the 99.5% confidence interval for mu.

1. A study investigated the possible link between body mass index (BMI) and plasma testosterone concentrations in a sample of 50 adolescent males between the ages of 14 and 20. Please see columns labeled BMI and testosterone in your HW5a spreadsheet.
2. Report the null and alternate hypothesis
3. Examine the assumptions of normality for the response variable as well as evenness of residuals (show and interpret a residual plot)
4. Show a scatterplot of the data with the best-fitting line
5. Report run the regression and report test statistic, df, and P value
6. Do you accept or reject the null? Interpret your results in one or two sentences.

7. BMI	Testosterone
   21.4	0.78
   19.0	0.70
   18.3	0.63
   19.5	0.60
   20.9	0.60
   23.4	0.69
   25.0	0.76
   24.1	0.58
   24.2	0.50
   22.6	0.48
   20.4	0.49
   16.2	0.43
   17.8	0.42
   21.0	0.38
   18.6	0.35
   20.9	0.35
   22.4	0.32
   23.5	0.31
   18.8	0.28
   19.3	0.25
   19.5	0.23
   20.2	0.24
   21.2	0.24
   21.3	0.26
   22.2	0.27
   28.3	0.30
   27.7	0.24
   28.1	0.19
   29.2	0.17
   33.3	0.18
   33.2	0.23
   34.7	0.24
   35.8	0.06
   37.0	0.15
   37.0	0.17
   39.0	0.18
   41.6	0.17
   42.4	0.15
   47.7	0.12
   45.7	0.25
   41.5	0.25
   38.0	0.25
   38.1	0.32
   37.8	0.35
   34.9	0.37
   34.8	0.39
   34.7	0.46
   32.0	0.49
   31.9	0.42
   30.5	0.36

A screening examination was performed on 250 persons for Factor X, which is found in disease Y. A definitive diagnosis for disease Y among the 250 persons had been obtained previously. The results of diagnoses are charted here:

Based on the information provided, which of the following expresses the sensitivity of this test?

A) 30%

B) 70%

C) 56%

D) 80%

Based on the information provided, which of the following expresses the specificity of this test?

A) 30%

B) 70%

C) 56%

D) 7%

Based on the information provided, the predictive value (+) is _____ and the predictive value (-) is__________.

A) 40%, 93%

B) 70%, 56%

C) 93% 40%

D) 56%, 70%

A study investigated if cell phone use impacted student drivers' reaction times. There were two groups: 29 students were assigned to the cell phone group while 29 students were assigned to the control group. The experiment measured the response time to traffic lights; for the cell phone group, the mean was 585.1 with a standard deviation of 88 and for the control group, the mean was 540 with a standard deviation of 65. Construct a 90% confidence interval for the difference in mean response times between the cell phone and control groups. Point Estimate: = Margin of Error: E = (round to 4 decimal places) Lower Limit: (round to 4 decimal places) Upper Limit: (round to 4 decimal places) We are 90 % confident that the true is between and .

Use a​ t-test to test the claim about the population mean μ at the given level of significance alphaα using the given sample statistics. Assume the population is normally distributed.

​Claim: μ= 51,800; alphaα= 0.05 

Sample​ statistics:

x overbar= 50,889​, s=2800​, n=18

What are the null and alternative​ hypotheses? Choose the correct answer below.

A.

H0​: μ= 51,800

Ha​: μ≠ 51,800

B.

H0​:μ≤ 51,800

Ha​: μ> 51,800

C.

H0​: μ ≥ 51,800

Ha​: μ < 51,800

D.

H0​: μ ≠ 51,800

Ha​: μ = 51,800

What is the value of the standardized test​ statistic?

The standardized test statistic is? ___ (round to two decimal places)

What​ is(are) the critical​ value(s)?

The critical​ value(s) is(are) _____ (round to three decimal places as needed.)

Decide whether to reject or fail to reject the null hypothesis.

A.

Fail to rejectFail to reject H0. There is not enough evidence to reject the claim.

B.

Reject H0. There is not enough evidence to reject the claim.

C.

Reject H0.

There is enough evidence to reject the claim.

D.

Fail to reject H0. There is enough evidence to reject the claim.

1. A researcher in a small town is interested in estimating the true proportion of adults in the town who smoke. 215 adults were randomly selected from the town, and it was found that 36 of them smoke. We would like to construct a 90% confidence interval estimate for the true proportion of adults in the town that smoke.

a. What are the values of ??/2, ?, ?̂, and ?̂? (Round ?̂and ?̂ to three decimal places if needed.) ??/2

Za/2= _______________ ? = _______________ ?̂= _______________ ?̂ = _______________

b. Calculate the margin of error (E) for a 90% confidence interval. (You must show the setup to receive credit. You may round to four decimal places if needed.) E = _______________

c. Construct the 90% confidence interval for the true proportion of smokers in the town. (Round limits to three decimal places.) _______________< ? < _______________

please show work and setup

An automobile manufacturer would like to know what proportion of its customers are not satisfied with the service provided by the local dealer. The customer relations department will survey a random sample of customers and compute a 90% confidence interval for the proportion who are not satisfied.

(a) Past studies suggest that this proportion will be about 0.21. Find the sample size needed if the margin of the error of the confidence interval is to be about 0.025.
(You will need a critical value accurate to at least 4 decimal places.)
Sample size:

(b) Using the sample size above, when the sample is actually contacted, 29% of the sample say they are not satisfied. What is the margin of the error of the confidence interval?

1. The table below contains the widths of a product, showing 10 samples of size 5 measurements each.

1. Construct a sample means, X control chart and R chart for the above data.
2. Identify those subgroup means which are outside the control limits.
3. Comment on the process.

Suppose an experiment was conducted to compare the fracture toughness of high-purity steel of some type with commercial-purity steel of the same type. For 9 high-purity specimens, the sample mean toughness and sample standard deviation of toughness (in some scale) were 1.82 and 0.6, respectively, whereas for 9 commercial-purity specimens, the sample mean and sample standard deviations were 2.43 and 0.82, respectively. Assume the data for both the high- and commercial-purity steels are normally distributed. Does this data suggest that the true mean toughness for the population of commercial-purity steel exceeds that of high-purity steel? To answer this question, state and test the appropriate hypotheses using a significance level of 0.05.

1. In a study on bromeliads (tropical epiphytic plants), researchers wanted to determine the effects of adding fertilizer on the growth rates of these plants (please see number of leaves and fertilizer columns on HW5b spreadsheet). They measured growth rate as the number of new leaves added to each plant after 7 months of fertilization. The four treatments were nitrogen, Phosphorus, both, neither. Which treatments have significant effects on the addition of new bromeliad leaves?

1. Set up an appropriate null and alternate hypothesis
2. Report an F statistic, df, and P value
3. do you accept or reject the null?
4. Run a Tukey’s test to determine where any differences occur. Display and interpret the results of this test.

5. number leaves	fertilizer
   15	n
   14	n
   15	n
   16	n
   17	n
   18	n
   17	n
   13	n
   14	p
   14	p
   14	p
   11	p
   13	p
   12	p
   15	p
   15	p
   14	both
   16	both
   15	both
   14	both
   14	both
   13	both
   17	both
   14	both
   11	neither
   13	neither
   16	neither
   15	neither
   15	neither
   11	neither
   12	neither