1.A random sample of size 120 is drawn from a large population with mean 38.75 obtain the sd of the distribution of all possible sample mean ( let the sample sd be s= 5.28 ) what is the sampling distribution of the mean?

2. In a random sample of size 506, the average cholesterol level of group of adults is 96.997 if the standard deviation of the colesterol level in the city adults population is 1.74 find the 72% confidence for u

Suppose the National Transportation Safety Board (NTSB) wants to examine the safety of compact cars, midsize cars, and full-size cars. It collects a sample of cars each of the cars types. The data below displays the frontal crash test performance percentages.

Patrick wants to purchase a new car, but he is concerned about safety ratings. Using the data from the chart above, what would you recommend to Patrick if he is debating between compact, midsize, and full-size cars? FYI: High scores on crash performance tests are GOOD. (Higher scores means they passed the test a higher percent of the time.)

1. Evaluate all three types of car in your response using One-Way ANOVA and follow-up t-tests. 2. Explain why you gave him this suggestion.

The survival rate of a cancer using an existing medication is known to be 30%. A pharmaceutical company claims that the survival rate of a new drug is higher. The new drug is given to 15 patients to test for this claim. Let X be the number of cures out of the 15 patients. Suppose the rejection region is {8 }.≥X a. State the testing hypotheses. b. Determine the type of error that can occur when the true survival rate is 25%. Find the error probability. c. Determine the type of error that can occur when the true survival rate is 30%. Find the error probability. d. Determine the type of error that can occur when the true survival rate is 40%. Find the error probability. e. What is the level of significance?

In 2009, the Southeastern Conference (SEC) commissioner set a goal to have greater than 65% of athletes that are entering freshmen graduate in 6 years. In 2015, a sample of 100 entering freshmen from 2009 was taken and it was found that 70 had graduated in 6 years. Does this data provide evidence that the commissioner’s graduation goal was met (α = .10)?

The value of the test statistic is ________ and the critical value is _________.

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)