Nurse             Pretest -Score            Post-test Score

A                                  63                                81

B                                  89                                90

C                                 76                                89

D                                 71                                76       

E                                  90                                90       
F                                  56                                78       
G                                 78                                82

- Conduct a t-test on the data and report your interpretation of the output.

The number of contaminants in samples of one cubic centimetre of polluted water has a Poisson distribution with a mean of 1.

a. What is the probability a sample will contain some (one or more) contaminants?

b. If four samples are independently selected from this water, find the probability that at least one sample will contain some (one or more) contaminants?

c. If 100 samples are selected instead, what is approximately the probability of seeing at least 60 samples with a contaminant? (Use the Normal table provided for your calculations)

1. Given a random variable X having a normal distribution with μ=50, and σ =10. The probability that Z assumes a value between 45 and 62 is: ___________.

Here are summary statistics for randomly selected weights of newborn​ girls: nequals193​, x overbarequals32.2 ​hg, sequals6.4 hg. Construct a confidence interval estimate of the mean. Use a 90​% confidence level. Are these results very different from the confidence interval 31.1 hgless thanmuless than33.1 hg with only 15 sample​ values, x overbarequals32.1 ​hg, and sequals2.1 ​hg?

What is the confidence interval for the population mean mμ​?

Are the results between the two confidence intervals very​ different?

In an experiment to compare two diets for fattening beef steers, nine pairs of animals were chosen from the herd: members of each pair were matched as closely as possible with respect to hereditary factors. The members of each pair were randomly allocated, one to each diet. The following table shows the weight gains (Ib) of the animals over a 140 day test period on diet 1 (Y1) and on diet 2 (Y2). Pair Diet 1 Diet 2 1 596 498 2 422 460 3 524 468 4 454 458 5 538 530 6 552 482 7 478 528 8 564 598 9 556 456 (A) Construct a 99% confidence interval for the difference in mean treating the samples as paired. (B) Interpret the confidence interval.

A genetic experiment with peas resulted in one sample of offspring that consisted of 404 green peas and 154 yellow peas.

a. Construct a 95​% confidence interval to estimate of the percentage of yellow peas.

b. It was expected that​ 25% of the offspring peas would be yellow. Given that the percentage of offspring yellow peas is not​ 25%, do the results contradict​ expectations?

Suppose X1; : : : ; Xn is i.i.d Exponential distribution with density
f(xjθ) = (1/θ) * e(-x/θ); 0 ≤ x < 1; θ > 0:
(a) Find the UMVUE (the best unbiased estimator) of θ.
(b) What is the Cramer-Rao lower bound of all unbiased estimator of all unbiased estimator
of θ. Does the estimator from (a) attain the lower bound? Justify your answer.
(c) What is the Cramer-Rao lower bound of all unbiased estimator of θ^2?
3
(d) Find the UMVUE of θ2. Does this estimator attain the lower bound in (c)?

The overhead reach distances of adult females are normally distributed with a mean of 205 cm and a standard deviation of 8.9 cm .

a. Find the probability that an individual distance is greater than 217.50 cm.

b. Find the probability that the mean for 15 randomly selected distances is greater than 202.80 cm

. c. Why can the normal distribution be used in part​ (b), even though the sample size does not exceed​ 30?

A simple random sample of size 44 has mean 3.01. The population standard deviation is 1.51. Construct a 90% confidence interval for the population mean.

1.The parameter is the population (choose one) mean, standard deviation, proportion, variance

2. The correct method to find the confidence interval is the (choose one) z, t, chi square method

1. A major automobile company claims that its New electric powered car has an average range of more than 100 miles. A random sample of 50 new electric cars was selected to test the claim. Assume that the population standard deviation is 12 miles. A 5% level of significance will be used for the test.

1. What would be the consequences of making a Type II error in this problem?

2. Compute the Probability of making a Type II error if the true population mean is 105 miles.

3. What is the maximum probability of making a Type I error in this problem?

A study of the pay of corporate chief executive officers (CEOs) examined the increase in cash compensation of the CEOs of 103 companies, adjusted for inflation, in a recent year. The mean increase in real compensation was x = 7.7%, and the standard deviation of the increases was s = 41%. Is this good evidence that the mean real compensation μ of all CEOs increased that year?

Because the sample size is large, the sample s is close to the population σ, so take σ = 41%.

(a) Sketch the normal curve for the sampling distribution of x when H_o is true. Shade the area that represents the P-value for the observed outcome x = 7.7%. (Do this on paper. Your instructor may ask you to turn in this work.)

(b) Calculate the P-value. (Round your answer to four decimal places.)


(c) Is the result significant at the α = 0.05 level? Do you think the study gives strong evidence that the mean compensation of all CEOs went up?

Reject the null hypothesis, there is significant evidence that the mean compensation of all CEOs went up.

Reject the null hypothesis, there is not significant evidence that the mean compensation of all CEOs went up.    

Fail to reject the null hypothesis, there is not significant evidence that the mean compensation of all CEOs went up.

Fail to reject the null hypothesis, there is significant evidence that the mean compensation of all CEOs went up.

please describe with examples the relationship between confidence intervals and hypothesis testing.

If n=560 and p' (p-prime) = 0.87, construct a 99% confidence interval.

Give your answers to three decimals.

A sample of final exam scores is normally distributed with a mean equal to 26 and a variance equal to 16.

(a) What percentage of scores are between 22 and 30? (Round your answer to two decimal places.)

(b)What raw score is the cutoff for the top 10% of scores? (Round your answer to one decimal place.)

(c)What is the proportion below 19? (Round your answer to four decimal places.)

(d)What is the probability of a score less than 33? (Round your answer to four decimal places.)

An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 130 engines and the mean pressure was 7.6 lbs/square inch. Assume the standard deviation is known to be 1. If the valve was designed to produce a mean pressure of 7.7 lbs/square inch, is there sufficient evidence at the 0.05 level that the valve does not perform to the specifications? State the null and alternative hypotheses for the above scenario.