In a study of fast food accuracy on drive-thru orders, Burger King had 264 accurate orders and 54 that were not accurate.

a. Construct a 95% CI for the percentage of orders that are not accurate.

b. A similar survey at McDonald's yield a 95% CI of inaccurate orders of 6.2%<P<15.9%. Comparing the two results, what do you find?

Many investors and financial analysts believe the Dow Jones Industrial Average (DJIA) gives a good barometer of the overall stock market. On January 31, 2006, 9 of the 30 stocks making up the DJIA increased in price (The Wall Street Journal, February 1, 2006). On the basis of this fact, a financial analyst claims we can assume that 30% of the stocks traded on the New York Stock Exchange (NYSE) went up the same day. A sample of 69 stocks traded on the NYSE that day showed that 25 went up. You are conducting a study to see if the proportion of stocks that went up is is significantly more than 0.3. You use a significance level of α = 0.05 α = 0.05 .

What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic =

What is the p-value for this sample? (Report answer accurate to four decimal places.)

p-value = The p-value is... less than (or equal to) α α greater than α α This test statistic leads to a decision to... reject the null accept the null fail to reject the null As such, the final conclusion is that... There is sufficient evidence to warrant rejection of the claim that the proportion of stocks that went up is is more than 0.3. There is not sufficient evidence to warrant rejection of the claim that the proportion of stocks that went up is is more than 0.3. The sample data support the claim that the proportion of stocks that went up is is more than 0.3. There is not sufficient sample evidence to support the claim that the proportion of stocks that went up is is more than 0.3.

Core i5 and i7 are two different types of CPU manufactured by Intel. As you may know as a matter of fact, Intel does not produce two types of CPUs. Instead, they just produce Core i7 chips. However, since a chip contains many millions of transistors, some of the transistors may not work properly, while other regions from the chip are working perfectly. In this case, Intel does not scrap the chip to trash, as it will be a waste, but deactivates the malfunctioning region and sell it as a cheaper chip, named Core i5, with less but perfectly functional features. Suppose an assembly line is able to manufacture 3000 chips per day. The probability that a chip meets the Core i7 standard is independently 1/1000. (While the background of this question is real, the probability here is much lower than the true probability.) An assembly line is qualified if it is able to produce at least 3 Core i7 per day. (a) Write down the exact expression of the probability that this assembly line is qualified if it operates only one day. (b) Write down a relevant approximate expression for the probability from (a).

Consider the assembly line described in the above question. Since Core i7 makes much more profit than Core i5, Intel decides to manufacture more chips in a day in order to produce sufficient Core i7 chips per day with high probability. Specifically, the CEO wants to get at least 3 Core i7 chips per day with probability at least 0.999. How many assembly lines should Intel purchase in total?

Since an instant replay system for tennis was introduced at a major​ tournament, men challenged 14301430 referee​ calls, with the result that 416416 of the calls were overturned. Women challenged 740740 referee​ calls, and 219219 of the calls were overturned. Use a 0.050.05 significance level to test the claim that men and women have equal success in challenging calls. Complete parts​ (a) through​ (c) below.

1. An experiment compared the ability of a group of chefs versus amateur cooks to taste spices in a dish. The researchers recorded the total number of spices each person identified and calculated the statistics below. Group n Mean Variance Chefs 10 8.3 1.3 Amateurs 10 5.5 3.1 (a) Calculate the 99% confidence interval for the difference between the means of the two groups. (b) Do you think the mean difference between the groups in the population could be 0.5? Why or why not? z-scores Confidence z Interval 80% 1.282 85% 1.440 90% 1.645 95% 1.960 99% 2.576 99.5% 2.807 99.9% 3.291 t-scores df 0.95 0.99 2 4.303 9.925 5 2.571 4.032 6 2.447 3.707 7 2.365 3.499 8 2.306 3.355 9 2.262 3.25 10 2.228 3.169 18 2.101 2.878 19 2.093 2.861 20 2.086 2.845 21 2.080 2.831

Consider arrangements of the letters NEWBIT. How many arrangements start or end with a vowel?

In 1940 the average size of a U.S. farm was 174 acres†. Let's say that the standard deviation was 56 acres. Suppose we randomly survey 46 farmers from 1940.

• Part (c)

  Give the distribution of

  X.

  (Round your standard deviation to two decimal places.)

  X

  ~ ,

• Part (d)

  The middle 50% of the distribution for X,
  the bounds of which form the distance represented by the IQR, lies between what two values? (Round your answers to two decimal places.)

  acres	(smaller value)
  acres	(larger value)

Jack packs 3 pairs of shoes, 4 pairs of boots, 6 pairs of jeans, 8 pairs of dress pants, and 2 dress shirts for a trip.

a.) How many different outfits can Jack make with these items?

b.) If Jack were to bring along 2 sweaters so that he could wear either a dress shirt or a sweater or he could wear both a dress shirt and a sweater, how many outfits could Jack make?

1. Overproduction of uric acid in the body can be an indication of cell breakdown. This may be an advance indication of illness such as gout, leukemia, or lymphoma.† Over a period of months, an adult male patient has taken fifteen blood tests for uric acid. The mean concentration was x = 5.35 mg/dl. The distribution of uric acid in healthy adult males can be assumed to be normal, with σ = 1.77 mg/dl.

(a) Find a 95% confidence interval for the population mean concentration of uric acid in this patient's blood. What is the margin of error? (Round your answers to two decimal places.)

(b) What conditions are necessary for your calculations? (Select all that apply.)

n is largeσ is knownuniform distribution of uric acidσ is unknownnormal distribution of uric acid

(c) Interpret your results in the context of this problem.

- There is a 95% chance that the confidence interval is one of the intervals containing the population average uric acid level for this patient.

-The probability that this interval contains the true average uric acid level for this patient is 0.95.     

-There is a 5% chance that the confidence interval is one of the intervals containing the population average uric acid level for this patient.

-The probability that this interval contains the true average uric acid level for this patient is 0.05.

-There is not enough information to make an interpretation.

(d) Find the sample size necessary for a 95% confidence level with maximal margin of error E = 1.10 for the mean concentration of uric acid in this patient's blood. (Round your answer up to the nearest whole number.)
blood tests

2. At Burnt Mesa Pueblo, archaeological studies have used the method of tree-ring dating in an effort to determine when prehistoric people lived in the pueblo. Wood from several excavations gave a mean of (year) 1251 with a standard deviation of 33 years. The distribution of dates was more or less mound-shaped and symmetric about the mean. Use the empirical rule to estimate the following.

(a) a range of years centered about the mean in which about 68% of the data (tree-ring dates) will be found
between  and  A.D.

(b) a range of years centered about the mean in which about 95% of the data (tree-ring dates) will be found
between  and  A.D.

(c) a range of years centered about the mean in which almost all the data (tree-ring dates) will be found
between  and  A.D.

3. Sketch the area under the standard normal curve over the indicated interval and find the specified area. (Round your answer to four decimal places.)

The area to the left of

z = −1.43 is ______

Group 1: Control - 20, 14, 18, 16, 17, 17

Group 2: Psychodynamic - 20, 9, 10, 15, 15, 15

Group 3: Rational-Emotive - 18, 7, 15, 9, 11, 12

Group 4: Behavior Modification - 15, 5, 6, 13, 12, 9

Use Tukey's HSD to compare the individual means.

What is q critical (from Table L)? (1 point)

What is MS within (a.k.a. MS error in some output)? (1 point)

What is n? (1 point)

Compute HSD. (1 point)

Are any of the four means statistically significantly different from the others? If so, which ones? ( 1 point)

A student randomly selected 70 packets of sugar and weighed the contents of each packet, getting a mean of 3.586 g and a standard deviation of 0.074 g. Test the claim that the weights of the sugar packets have a mean equal to 3.5 g, as indicated on the label.

1.   Copy and paste the Minitab output for exercise into the document underneath the problem.   You are not also required to do these by hand, unless you want to.  

2. Write the rejection rule word for word as written here, "Reject Ho if the p-value is less than or equal to alpha."

3.   Write the actual p-value and alpha, then either "Reject Ho" or "Do not reject Ho." As an example: 0.0021 ≤ 0.05. True. Reject Ho.

4.    Write an English sentence stating the conclusion, claim, and significance level. As an example: If the claim is "Can we conclude that male business executives are taller, on the average, than the general male population at the  α  = 0.05 level?", and if we found our conclusion to be do not reject Ho, the sentence would be, "There is not enough evidence to conclude that  male business executives are taller, on the average, than the general male population at the  α  = 0.05 level."

A sample of 34 observations is selected from a normal population. The sample mean is 30, and the population standard deviation is 3. Conduct the following test of hypothesis using the 0.05 significance level:

H₀: μ = 31

H₁: μ ≠ 31

a. Is this a one- or two-tailed test?

(Click to select)  One-tailed test  Two-tailed test

b. What is the decision rule?

Reject H₀ and accept H₁ when z does not lie in the region from  to  .

c. What is the value of the test statistic? (Negative answer should be indicated by a minus sign. Round the final answer to 2 decimal places.)

Value of the test statistic           

d. What is your decision regarding H₀?

(Click to select)  Fail to reject  Reject  H₀

e. What is the p-value? (Round the final answer to 4 decimal places.)

The p-value is             .

A student wants to test whether today’s graduating seniors are just as optimistic about their future prospects than in the past. Data from a similar survey given 10 years ago to a national sample of graduating students resulted in a mean of 7.9. A random sample of 16 seniors is asked to evaluate the future job marked on a 10-point scale from 1 (dismal) to 10 (excellent). The scores on the test are: 10, 6, 6, 8, 9, 7, 8, 6, 7, 8, 8, 7, 6, 9, 5, 10.

(a) Set up your hypotheses using the correct notation

(b) Compute tobt

(c) What is the statistical decision? JUSTIFY YOUR ANSWER

(d) What is the conclusion?

(e) Compute the 95% Confidence Interval for μ

A population has standard deviation 17.7.

Part 1 of 2
(a) How large a sample must be drawn so that a 90% confidence interval for u will have a margin of error equal to 3.2?
Round the critical value to no less than three decimal places. Round the sample size up to the nearest integer.

A sample size of ___ is needed to be drawn in order to obtain a 90% confidence interval with a margin of error equal to 3.2.

Part 2 of 2
(b) If the required confidence level were 99.5, would the necessary sample size be larger or smaller

(larger/smaller), because the confidence level is (higher/lower).