n = 5 p or π = 0.15 P(X<2) =

The housing market has recovered slowly from the economic crisis of 2008.​ Recently, in one large​ community, realtors randomly sampled 32 bids from potential buyers to estimate the average loss in home value. The sample showed the average loss was ​$8251 with a standard deviation of ​$1739 .Find a 90​% confidence interval for the mean loss in value per home. ​Answer should be= ($__, $__)

Education. Post-secondary educational institutions in the United States (trade schools, colleges, universities, etc.) traditionally offer four different types of degrees or certificates. The U.S. Department of Education recorded the highest degree granted by each of these institutions in the year 2003. The percentages are shown in the table below. A random sample of 225 institutions was taken in 2013 and the number of institutions in the sample for each category is also shown in the table. Conduct a hypothesis test to determine whether there has been any change from the percentages reported in 2003. Round all calculated values to four decimal places.

a. Enter the expected values for the hypothesis test in the table below.

b. Calculate the test statistic for this hypothesis test.  ? z t X^2 F  =

c. Calculate the degrees of freedom for this hypothesis test.

d. Calculate the p-value for this hypothesis test. p-value =

e. Based on the p-value, we have:
A. little evidence
B. strong evidence
C. very strong evidence
D. some evidence
E. extremely strong evidence
that the null model is not a good fit for our observed data.

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 =