A large cooperation has quality control over its fertilizers. The fertilizes are composed of nitrogen. The fertilizer requires 3 mg of nitrogen. The distribution of the percentage of nitrogen is unknown with a mean of 2.5 mg and a standard deviation of 0.1. A specialist randomly checked 100 fertilizer samples.

What is the probability that the mean of the sample of 100 fertilizers less than 2 mg?

Let a random sample of 100 homes sold yields a sample mean sale price of $100,000 and a sample standard deviation of $5,000. Find a 99% confidence interval for the average sale price given the information provided above.

Calculate the following:

1) Margin of error = Answer

2) x̄ ± margin error = Answer < μ < Answer

Table1 -

Common Z-values for confidence intervals

Confidence Level Zα/2

90% 1.645

95% 1.96

99% 2.58

A sample of 35 two-year colleges in 2012-2013 had a mean tuition (for in-state undergraduate students) of $2918. The true standard deviation of the tuition for these schools is known to be $1079.

Calculate a 90% confidence interval for the average in-state tuition of all two-year colleges in 2012-2013.

Suppose that the number of drivers who travel between a particular origin and destination during a designated time period has a Poisson distribution with parameter μ = 20 (suggested in the article "Dynamic Ride Sharing: Theory and Practice"†). (Round your answer to three decimal places.)

(a)

What is the probability that the number of drivers will be at most 13?

(b)

What is the probability that the number of drivers will exceed 26?

(c)

What is the probability that the number of drivers will be between 13 and 26, inclusive?

What is the probability that the number of drivers will be strictly between 13 and 26?

(d)

What is the probability that the number of drivers will be within 2 standard deviations of the mean value?

college professor never finishes his lecture before the end of the hour and always finishes his lectures within 3 min after the hour. Let X = the time that elapses between the end of the hour and the end of the lecture and suppose the pdf of X is as follows.

f(x)= kx^2 0 less than or equal to x less than or equal to 3 otherwise f(x)=0

a) find the value of K that satisfy condition of PDF?

b) find cdf (cumulative distributive function) for f(x)

c) what is the probability that the lecture ends at t=0.5min of the end of the hour?

also explain how you would put it in a calculator using normpdf/binompdf or normcdf/binomcdf

The article "Plugged In, but Tuned Out"† summarizes data from two surveys of kids age 8 to 18. One survey was conducted in 1999 and the other was conducted in 2009. Data on number of hours per day spent using electronic media that are consistent with summary quantities given in the article are given below (the actual sample sizes for the two surveys were much larger). For purposes of this exercise, assume that it is reasonable to regard the two samples as representative of kids age 8 to 18 in each of the 2 years that the surveys were conducted.
2009   5   9   5   8   7   6   7   9   7   9   6   9   10   9   8
1999   4   5   7   7   5   7   5   6   5   6   7   8   5   6   6

(a)
Because the given sample sizes are small, in order for the two-sample t test to be appropriate, what assumption must be made about the distributions of electronic media use times?
o We need to assume that the population distribution in 1999 of time per day using electronic media are normal.
o We need to assume that the population distribution in 2009 of time per day using electronic media are normal.
o We need to assume that the population distributions in both 1999 and 2009 of time per day using electronic media are normal.
o We need to assume that the population distribution in either 1999 or 2009 of time per day using electronic media is normal.

Use the given data to construct graphical displays that would be useful in determining whether this assumption is reasonable. Do you think it is reasonable to use these data to carry out a two-sample t test?
o The boxplot of the 2009 data is roughly symmetrical with no outliers, so the assumption is reasonable.
o Both the boxplot of the 1999 data and the 2009 data are skewed to the right, so the assumption is not reasonable.
o The boxplot of the 1999 data is roughly symmetrical with no outliers, so the assumption is reasonable.
o Boxplots of the both the 1999 data and 2009 data are roughly symmetrical with no outliers, so the assumption is reasonable.
o The boxplot of the 1999 data has an outlier to the far right, so the assumption is not reasonable.

(b)
Do the given data provide convincing evidence that the mean number of hours per day spent using electronic media was greater in 2009 than in 1999? Test the relevant hypotheses using a significance level of 0.01. (Use a statistical computer package to calculate the P-value. Use μ2009 − μ1999. Round your test statistic to two decimal places, your df down to the nearest whole number, and your P-value to three decimal places.)
t   =  
df   =  
P-value   =  

State your conclusion.
o Reject H0. There is convincing evidence that the mean number of hours per day spent using electronic media was greater in 2009 than in 1999.
o Fail to reject H0. There is convincing evidence that the mean number of hours per day spent using electronic media was greater in 2009 than in 1999.
o Fail to reject H0. There is not convincing evidence that the mean number of hours per day spent using electronic media was greater in 2009 than in 1999.
o Reject H0. There is not convincing evidence that the mean number of hours per day spent using electronic media was greater in 2009 than in 1999.

(c)
Construct and interpret a 98% confidence interval estimate of the difference between the mean number of hours per day spent using electronic media in 2009 and 1999. (Use μ2009 − μ1999. Round your answers to two decimal places.)

_______ to _______ hours

Interpret the interval.
o We are 98% confident that the true difference in mean number of hours per day spent using electronic media in 2009 and 1999 is between these two values.
o We are 98% confident that the true mean number of hours per day spent using electronic media in 2009 is between these two values.
o We are 98% confident that the true mean number of hours per day spent using electronic media in 1999 is between these two values.
o There is a 98% chance that the true mean number of hours per day spent using electronic media in 2009 is directly in the middle of these two values.
o There is a 98% chance that the true difference in mean number of hours per day spent using electronic media in 2009 and 1999 is directly in the middle of these two values.

(everything bold needs an answer)

Brand loyalty and the Chicago Cubs. According to literature on brand loyalty, consumers who are loyal to a brand are likely to consistently select the same product. This type of consistency could come from a positive childhood association. To examine brand loyalty among fans of the Chicago Cubs, 371 Cubs fans among patrons of a restaurant located in Wrigleyville were surveyed prior to a game at Wrigley Field, the Cubs’ home field.34 The respondents were classified as “die-hard fans” or “less loyal fans.” Of the 134 die-hard fans, 90.3% reported that they had watched or listened to Cubs games when they were children. Among the 237 less loyal fans, 67.9% said that they had watched or listened as children.

(a) Find the numbers of die-hard Cubs fans who watched or listened to games when they were children. Do the same for the less loyal fans.

(b) Use a significance test to compare the die-hard fans with the less loyal fans with respect to their childhood experiences relative to the team.

(c) Express the results with a 95% confidence interval for the difference in proportions.

Brand loyalty in action. The study mentioned
in the previous exercise found that two-thirds of the die-hard fans attended Cubs games at least once a month, but only 20% of the less loyal fans attended this often. Analyze these data using a significance test and a confidence interval. Write a short summary of your findings.

A sample of blood pressure measurements is taken from a data set and those values​ (mm Hg) are listed below. The values are matched so that subjects each have systolic and diastolic measurements. Find the mean and median for each of the two samples and then compare the two sets of results. Are the measures of center the best statistics to use with these​ data? What else might be​ better? ​Systolic: 150 126 95 140 154 159 145 101 152 135 ​Diastolic: 60 83 53 68 79 76 91 57 55 86 Find the means. The mean for systolic is nothing mm Hg and the mean for diastolic is nothing mm Hg. ​(Type integers or decimals rounded to one decimal place as​ needed.) Find the medians. The median for systolic is nothing mm Hg and the median for diastolic is nothing mm Hg. ​(Type integers or decimals rounded to one decimal place as​ needed.) Compare the results. Choose the correct answer below. A. The mean and median appear to be roughly the same for both types of blood pressure. B. The mean and the median for the systolic pressure are both lower than the mean and the median for the diastolic pressure. C. The mean and the median for the diastolic pressure are both lower than the mean and the median for the systolic pressure. D. The median is lower for the diastolic​ pressure, but the mean is lower for the systolic pressure. E. The mean is lower for the diastolic​ pressure, but the median is lower for the systolic pressure. Are the measures of center the best statistics to use with these​ data? A. Since the sample sizes are​ large, measures of center would not be a valid way to compare the data sets. B. Since the sample sizes are​ equal, measures of center are a valid way to compare the data sets. C. Since the systolic and diastolic blood pressures measure different​ characteristics, a comparison of the measures of center​ doesn't make sense. D. Since the systolic and diastolic blood pressures measure different​ characteristics, only measures of center should be used to compare the data sets. What else might be​ better? A. Since measures of center are​ appropriate, there would not be any better statistic to use in comparing the data sets. B. Because the data are​ matched, it would make more sense to investigate any outliers that do not fit the pattern of the other observations. C. Since measures of center would not be​ appropriate, it would make more sense to talk about the minimum and maximum values for each data set. D. Because the data are​ matched, it would make more sense to investigate whether there is an association or correlation between the two blood pressures.

I ran some test about something truly exciting and found that for Group A, the sample meanis 8.5, the standard deviationis 0.6, for n = 12. For Group B, the sample meanis 7.7, the standard deviationis 0.8, and n = 15. Use these values (which you will need to manipulate to suit your needs!) for #1-3. Yes, this is all the info you need!

1. Calculate the effect size using Cohen’s d.

2. Calculate the amount of variance accounted for using r².

3. Construct a 95% confidence interval to estimate the true difference between the groups. Is there one?

In this problem, assume that the distribution of differences is approximately normal. Note: For degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value by a small amount and therefore produce a slightly more "conservative" answer. Suppose that at five weather stations on Trail Ridge Road in Rocky Mountain National Park, the peak wind gusts (in miles per hour) for January and April are recorded below. Wilderness District 1 2 3 4 5 January 133 122 134 64 78 April 110 97 107 88 61 Does this information indicate that the peak wind gusts are higher in January than in April? Use α = 0.01. Solve the problem using the critical region method of testing. (Let d = January − April. Round your answers to three decimal places.) test statistic = critical value =

You are still trying to estimate the girth of Kerrville toads. You collect 100 toads from many different ponds, rivers, witches cauldrons, etc around Kerrville. This is in the data set data("toad_girth") in my package. Using this data set find a 95% confidence interval for the population standard deviation of the toad girths:

In a study of the accuracy of fast food​ drive-through orders, one restaurant had 32 orders that were not accurate among 398 orders observed. Use a 0.10 significance level to test the claim that the rate of inaccurate orders is equal to​ 10%. Does the accuracy rate appear to be​ acceptable?

Identify the null and alternative hypotheses for this test. Choose the correct answer below.

A. H0​: p≠0.1 H1​: p=0.1

B. H0​: p=0.1 H1​: p≠0.1

C. H0​: p=0.1 H1​: p<0.1

D. H0​: p=0.1 H1​: p>0.1

Identify the test statistic for this hypothesis test.

The test statistic for this hypothesis test is _____ (Round to two decimal places as​ needed.)

Identify the​ P-value for this hypothesis test.

The​ P-value for this hypothesis test is _____ ​(Round to three decimal places as​ needed.)

Identify the conclusion for this hypothesis test.

A. Reject H0. There is not sufficient evidence to warrant rejection of the claim that the rate of inaccurate orders is equal to​ 10%.

B. Fail to reject H0. There is sufficient evidence to warrant rejection of the claim that the rate of inaccurate orders is equal to​ 10%.

C. Reject H0. There is sufficient evidence to warrant rejection of the claim that the rate of inaccurate orders is equal to​ 10%.

D. Fail to reject H0. There is not sufficient evidence to warrant rejection of the claim that the rate of inaccurate orders is equal to​ 10%.

Does the accuracy rate appear to be​ acceptable?

A. Since there is sufficient evidence to disprove the theory that the rate of inaccurate orders is equal to​ 10%, the accuracy rate is acceptable.

B. Since there is not sufficient evidence to disprove the theory that the rate of inaccurate orders is equal to​ 10%, it is possible that the accuracy rate is acceptable.

C. Since there is sufficient evidence to disprove the theory that the rate of inaccurate orders is equal to​ 10%, the accuracy rate is not acceptable. The restaurant should work to lower that rate.

D. Since there is not sufficient evidence to disprove the theory that the rate of inaccurate orders is equal to​ 10%, the accuracy rate is not acceptable. The restaurant should work to lower that rate

Paired sample test, (1) construct a 95% confidence interval and (2) conduct a t-test (α = 5%). This is to report to the NFL commisioner regarding points scored vs points allowed.

Data sets below

The developers of a new online game have determined from preliminary testing that the scores of players on the first level of the game can be modelled satisfactorily by a Normal distribution with a mean of 185 points and a standard deviation of 28 points. They would like to vary the difficulty of the second level in this game, depending on the player’s score in the first level.

(a) The developers have decided to provide different versions of the second level for each of the following groups:

(i) those whose score on the first level is in the lowest 25% of scores

ii) those whose score on the first level is in the middle 50% of scores

(iii) those whose score on the first level is in the highest 25% of scores. Use the information given above to determine the cut-off scores for these groups. (You may round each of your answers to the nearest whole number.)

(b) In the second level of the game, the developers have also decided to give players an opportunity to qualify for a bonus round. Their stated aim is that players from group (i) should have 75% chance of qualifying for the bonus round, players from group (ii) should have 55% chance of qualifying for the bonus round and that players from group (iii) should have 30% chance of qualifying for this round. Let ?, ? and ? respectively denote the events that a player’s score on the first level was in the lowest 25% of scores, the middle 50% of scores and the highest 25% of scores, and let ? denote the event that the player qualifies for the bonus round. Use event notation to express the developers’ aim as a set of conditional probabilities.

(c) Based on the developers’ stated aim, find the total probability that a randomly chosen player will qualify for the bonus round.

(d) Given that a player has qualified for the bonus round, what is the probability that the player’s score on the first level was in the middle 50% of scores for that level?

(e) Given that a player has not qualified for the bonus round, what is the probability that the player’s score on the first level was in the lowest 25% of scores for that level?