A television sports commentator wants to estimate the proportion of citizens who​ "follow professional​ football." Complete parts​ (a) through​ (c). ​(a) What sample size should be obtained if he wants to be within 2 percentage points with 94​% confidence if he uses an estimate of 52​% obtained from a​ poll? The sample size is nothing. ​(Round up to the nearest​ integer.) ​(b) What sample size should be obtained if he wants to be within 2 percentage points with 94​% confidence if he does not use any prior​ estimates? The sample size is nothing. ​(Round up to the nearest​ integer.) ​(c) Why are the results from parts​ (a) and​ (b) so​ close? A. The results are close because 0.52 left parenthesis 1 minus 0.52 right parenthesis equals0.2496 is very close to 0.25. B. The results are close because the confidence 94​% is close to​ 100%. C. The results are close because the margin of error 2​% is less than​ 5%.

A statistics professor gave a 5-point quiz to the 50 students in his class. Scores on the quiz could range from 0 to 5: The following frequency table resulted: (1.5 points)

1. Compute the values that define the following percentiles:

a. 25^th   2     b. 50^th   3     c. 55^th   3    d. 75^th   4e. 80^th   4     f. 99^th    5    

2. What is the interquartile range of the data in #1?

3. Compute the exact percentile ranks that correspond to the following scores:

a. 2        b. 3        c. 4        d. 1   

Daily high temperatures in St. Louis for the last week were as​ follows: 92​, 94​, 93​, 95​, 95​, 86​, 95 ​(yesterday).

​a) The high temperature for today using a​ 3-day moving average ​= 92

degrees ​(round your response to one decimal​ place).

​b) The high temperature for today using a​ 2-day moving average ​= 90.5

degrees ​(round your response to one decimal​ place).

​c) The mean absolute deviation based on a​ 2-day moving average​ = 3.3

degrees ​(round your response to one decimal​ place).

​d) The mean squared error for the​ 2-day moving average​ = ____ degrees²???

​(round your response to one decimal​ place).

suppose that 65% of all registered voters in an area favor a certain policy. Among 225 randomly selected registered voters, find the following:

P(x ≤ 150)

, the probability that at most 150 favor the policy? Round to two decimal places.

P(x ≥ 140)

, the probability that at least 140 favor the the policy? Round to two decimal places.

3. A recent study showed that the average number of sticks of gum a person chews in a week is 15. A college student believes that the guys in his dormitory chew less gum in a week. He conducts a study and samples 14 of the guys in his dorm and finds that on average they chew 13 sticks of gum in a week with a standard deviation of 3.6. Test the college student's claim at αα=0.01.

Since the level of significance is 0.01 the critical value is -2.65

The test statistic is: (round to 3 places)

The p-value is: (round to 3 places)

4. A recent publication states that the average closing cost for purchasing a new home is $8859. A real estate agent believes the average closing cost is more than $8859. She selects 22 new home purchases and finds that the average closing costs are $8747 with a standard deviation of $107. Help her decide if she is correct by testing her claim at αα=0.05.

Since the level of significance is 0.05 the critical value is 1.721

The test statistic is: (round to 3 places)

The p-value is: (round to 3 places)

5. A new baker is trying to decide if he has an appropriate price set for his 3 tier wedding cakes which he sells for $81.85. He is particullarly interested in seeing if his wedding cakes sell for less than the average price. He searches online and finds that out of 43 of the competitors in his area they sell their 3 tier wedding cakes for $82.38. From a previous study he knows the standard deviation is $6.98. Help the new baker by testing this with a 0.01 level of significance.

Since the level of significance is 0.01 the critical value is 2.326

The test statistic is: (round to 3 places)

The p-value is: (round to 3 places)

A technician compares repair costs for two types of microwave ovens (type I and type II). He believes that the repair cost for type I ovens is greater than the repair cost for type II ovens. A sample of 60 type I ovens has a mean repair cost of $76.43$, with a standard deviation of $17.12. A sample of 46 type II ovens has a mean repair cost of $69.23, with a standard deviation of $19.14. Conduct a hypothesis test of the technician's claim at the 0.05 level of significance. Let μ1 be the true mean repair cost for type I ovens and μ2 be the true mean repair cost for type II ovens.

State the null and alternative hypotheses for the test.

Compute the value of the test statistic. Round your answer to two decimal places.

Determine the decision rule for rejecting the null hypothesis H0H0. Round the numerical portion of your answer to three decimal places.

Make the decision for the hypothesis test.

a) What is the probability that a hand of 13 cards contains four of a kind (e.g., four 5’s, four Kings, four aces, etc.)?

b) A single card is randomly drawn from a thoroughly shuffled deck of 52 cards. What is the probability that the drawn card will be either a diamond or a queen?

c) The probability that the events A and B both occur is 0.3. The individual probabilities of the events A and B are 0.7 and 0.5. What is the probability that neither event A nor event B occurs?

Suppose a bank quotes S = $1.1045/€. The annualized risk-free interest rates are 4% and 6% in the U.S and Germany, respectively. Find the approximate forward rate for the euro. Do not write any symbol. Make sure to round your answers to the nearest 100th decimal points. For example, write 1.2345 for $1.2345/€.

Suppose a bank quotes $/€ = 1.1045-1.1506. What is the bid-ask spread in percentage? Do not write any symbol. Express your answers as a percentage. Make sure to round your answers to the nearest 100th decimal points. For example, write 12.34 for 12.34%.

1)A new chemical has been found to be present in the human bloodstream, and a medical group would like to study the presence of this chemical in some samples of patients. The presence of the chemical in a patient is measured by a score representing the 'parts per billion' in which that chemical appears in the blood. It is known that, on this scale, men have an average score of 810.9 and a standard deviation of 58. It is also known that women have an average score of 835.48 and a standard deviation of 21.

An assistant in the medical team has been handed a sample of 100 scores. The assistant knows that all of the scores are from one of the two genders, but the sample was not documented very well and so they do not which gender this is. Within the sample, the mean score is 825.4.

a)Complete the following statements. Give your answers to 1 decimal place.

If the sample came from a group of 100 men, then the sample mean is ______ standard deviations above the mean of the sampling distribution. In contrast, if the sample came from a group of 100 women, then the sample mean is _______ standard deviations below the mean of the sampling distribution.

b)Based on this, the assistant is more confident that the sample came from a group of 100 _____men or women_____

2)The life span at the birth of humans has a mean of 87.74 years and a standard deviation of 17.76 years. Calculate the upper and lower bounds of an interval containing 95% of the sample mean life spans at birth based on samples of 105 people. Give your answers to 2 decimal places.

a)Upper bound = _________ years

b)Lower bound = ______ years

3)A drug made by a pharmaceutical company comes in tablet form. Each tablet is branded as containing 120 mg of the particular active chemical. However, variation in manufacturing results in the actual amount of the active chemical in each tablet following a normal distribution with mean 120 mg and standard deviation 1.665 mg.

a)Calculate the percentage of tablets that will contain less than 119 mg of the active chemical. Give your answer as a percentage to 2 decimal places.

Percentage = %

b)Suppose samples of 12 randomly selected tablets are taken and the amount of active chemical measured. Calculate the percentage of samples that will have a sample mean of less than 119 mg of the active chemical. Give your answer as a percentage to 2 decimal places.

Percentage = %

4)

During its manufacturing process, Fantra fills its 20 fl oz bottles using an automated filling machine. This machine is not perfect and will not always fill each bottle with exactly 20 fl oz of soft drink. The amount of soft drink poured into each bottle follows a normal distribution with mean 20 fl oz and a standard deviation of 0.17 fl oz.

The Fantra quality testing department has just carried out a routine check on the average amount of soft drink poured into each bottle. A sample of 25 bottles was randomly selected and the amount of soft drink in each bottle was measured. The mean amount of soft drink in each bottle was calculated to be 19.90 fl oz. The Fantra Chief Executive Officer believes that such a low mean is not possible and a mistake must have been made.

Calculate the probability of obtaining a sample mean below 19.90 fl oz. Give your answer as a decimal to 4 decimal places.

probability =

The type of household for the U.S. population and for a random sample of 411 households from a community in Montana are shown below.

Use a 5% level of significance to test the claim that the distribution of U.S. households fits the Dove Creek distribution.

(a) What is the level of significance?


State the null and alternate hypotheses.

H₀: The distributions are different.
H₁: The distributions are the same.

H₀: The distributions are different.
H₁: The distributions are different.    

H₀: The distributions are the same.
H₁: The distributions are different.

H₀: The distributions are the same.
H₁: The distributions are the same.

(b) Find the value of the chi-square statistic for the sample. (Round the expected frequencies to two decimal places. Round the test statistic to three decimal places.)


Are all the expected frequencies greater than 5?

Yes

No    

What sampling distribution will you use?

uniform

chi-square    

binomial Student's t

normal

What are the degrees of freedom?


(c) Find or estimate the P-value of the sample test statistic. (Round your answer to three decimal places.)


(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis that the population fits the specified distribution of categories?

Since the P-value > α, we fail to reject the null hypothesis.

Since the P-value > α, we reject the null hypothesis.    

Since the P-value ≤ α, we reject the null hypothesis.

Since the P-value ≤ α, we fail to reject the null hypothesis.

(e) Interpret your conclusion in the context of the application.

At the 5% level of significance, the evidence is sufficient to conclude that the community household distribution does not fit the general U.S. household distribution.

At the 5% level of significance, the evidence is insufficient to conclude that the community household distribution does not fit the general U.S. household distribution.

Political polling relies heavily on sampling techniques, which allow us to make inferences about an entire population based on only a portion of the population. However, the "Brexit" referendum in the United Kingdom and several elections in the United States since 2016 have called into question the accuracy of much political polling

1. What explains the inaccuracy of many pre-election polling data since 2016? Provide specific case examples.

2. What statistical techniques could be used to improve the accuracy of polling?

3. Has the value of political polling diminished? What is your personal perception of political polling?

In each of the following sets of variables, which are likely candidates to be treated as independent and which as dependent within a research study?

• Gender, alcohol consumption, and driving record In the following set of variables

• High school GPA (grade point average), university freshman year GPA, choice of university major (selected before enrollment), race/ethnicity, and gender

• Age, race/ethnicity, smoking habits, and occurrence of breast cancer

Explain each answer please.

The administration of a local college states that the average age of its students is 28 years. Records of a random sample of 100 students give a mean age of 31 years. Using a population standard deviation of 10 years, test at the 5% significance level whether there is evidence that the administration’s statement is incorrect.

State clearly your null and alternative hypotheses.

Imagine you take the SAT which has a µ = 500 and σ = 100 and receive a score of X = 600. What proportion of people did better than you?

(round to two decimals)

EXPLAIN HOW YOU GOT THE ANSWER

A student asked 7 random people that graduated last year their GPA and starting salary. The following table includes the responses:

1. What is the coefficient of correlation?

a) -0.9857

b) -0.5854

c) 0.5854

d) 0.9857

2.  What is the slope of the regression equation?

a) 5.85

b) 7.81

c) 16.78

d) 67.85

3.  What is the regression equation?

a) GPA=7.81 + 14.57*$Starting Salary

b) GPA = 16.58+0.648*$Starting Salary

c) $Starting Salary=0.6048 + 16.58*GPA

d) $Starting Salary = 14.57 +7.81*GPA

3. Based on the data above what does the R² correlation coefficient indicate?

a) There is a positive linear relationship between GPA and starting salary.

b) This is not a good model for this data.

c) This is a fairly strong model for this data.

d) Both a and c.