The percent of fat calories that a person in America consumes each day is normally distributed with a mean of about 36 and a standard deviation of about ten. Suppose that 16 individuals are randomly chosen.

(a) For the group of 16, find the probability that the average percent of fat calories consumed is more than thirty-five (Round to 3 decimal places)

(b) Find the first quartile for the percent of fat calories.

(c) Find the first quartile for the average percent of fat calories.

The following data on price ($) and the overall score for 6 stereo headphones that were tested by Consumer Reports were as follows.

a. Does the t test indicate a significant relationship between price and the overall score?

The test t-Conclusion at α = .05

t =  (to 2 decimal places.)

p-value is - Select your answer -less than .02between .02 and .05between .05 and .1between .1 and .2greater than .2Item 2

What is your conclusion? Use α = .05.
- Select your answer -There is a significant relationship between price and overall scoreThere is no significant relationship between price and overall scoreItem 3 .

b. Test for a significant relationship using the F test.
p-value is - Select your answer -less than .01between .01 and .025between .025 and .05between .05 and .1greater than .1Item 4

What is your conclusion? Use α = .05.

Because p-value is - Select your answer -greater than or equal toless than or equal toequal toItem 5 .05, we - Select your answer -acceptrejectItem 6 H₀: β₁ is - Select your answer -greater than or equal to zeroless than or equal to zeroequal to zeroItem 7 .

c. Show the ANOVA table for these data. Round your answers to three decimal places, if necessary.

In August 2003, 56% of all employed adults in the United States reported that basic mathematical skills were critical or very important to their job. A researcher believes that this proportion has increased, so a random sample of 480 employed adults was taken and 297 of them felt that basic mathematical skills are critical or very important to their job.

Be sure to check if the conditions are met, and show how you checked them - show ALL work.

1a) Is there sufficient evidence to conclude that the percentage of all employed adults who feel basic mathematical skills are critical or very important to their job has increased? Use a significance level of α =0.05.

whats your conclusion?

1b) Find a 90% confidence interval for the proportion of all employed adults in the United States who feel that basic mathematical skills are critical or very important to their job. State your answer in words:

1c) How large of a sample would be needed in order to have a margin of error E=3% and a confidence level of 98%? sample size n=?

A researcher wishes to estimate the proportion of adults who have high speed internet access. What size sample should be obtained if she wishes the estimate to be within .03 with 99% confidence if a) she uses a previous estimate of .58? b) she does not use any prior estimate?

To test H0: mu=60 versus H1: mu<60, a random sample size n=25 is obtained from a population that is known to be normally distributed. Complete parts a through d below. a) if x bar= 57.4 and s= 14.1, compute the test statistic. b)If the researcher decides to test this hypothesis at the confidence variable= .1 level of significance, determine the critical value(s). c)draw the t-distribution that depicts the critical region. d)will the researcher reject the null hypothesis?

You wish to test the following claim (Ha) at a significance level of α=0.02

      Ho:p1=p2
      Ha:p1>p2

You obtain 118 successes in a sample of size n1=249 from the first population. You obtain 76 successes in a sample of size n2=242 from the second population. For this test, you should NOT use the continuity correction, and you should use the normal distribution as an approximation for the binomial distribution.

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

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

The test statistic is...

• in the critical region
• not in the critical region

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 first population proportion is greater than the second population proportion.
• There is not sufficient evidence to warrant rejection of the claim that the first population proportion is greater than the second population proportion.
• The sample data support the claim that the first population proportion is greater than the second population proportion.
• There is not sufficient sample evidence to support the claim that the first population proportion is greater than the second population proportion.

Please show all work and use ti84

The data show the population (in thousands) for a recent year of a sample of cities in South Carolina.

Source: U.S. Census Bureau.

Find the data value that corresponds to each percentile.

a. 40th percentile

b. 75th percentile

c. 90th percentile

d. 30th percentile

Using the same data, find the percentile corresponding to the given data value.

e. 27

f. 40

g. 58

h. 67

A number of minor automobile accidents occur at various high-risk intersections in York county despite the traffic lights. The traffic department claims that a modification in the type of light will reduce these accidents. The county commissioners have agreed to a proposed experiment. Eight intersections were chosen at random, and lights at those intersections were modified. The number of minor accidents during a six-months periods before and after the modifications were

At the .01 significance level, it is reasonable to conclude that the modifications reduced the number of traffic accidents?

Assume n independent observations, denoted Xi, (i=1,....n), are taken from a distribution with a mean of E(X)=μ and variance V(X) =σ2. Prove that the mean of the n observations has an expected value of E(X)=μ and a variance of V(X) =σ2/n. Use the appropriate E and V rules in your answer. What happens as n becomes large? What does this tell you about the quality of the sample mean as an estimate of μ as the sample size increases?

Triangulation is the process of examining data and other factors from different perspectives to establish a study’s validity.

What is your interpretation of validity in qualitative research? How should researchers use triangulation to establish validity in your qualitative concept paper?

Allen's hummingbird (Selasphorus sasin) has been studied by zoologist Bill Alther.† Suppose a small group of 13 Allen's hummingbirds has been under study in Arizona. The average weight for these birds is x = 3.15 grams. Based on previous studies, we can assume that the weights of Allen's hummingbirds have a normal distribution, with σ = 0.36 gram. When finding an 80% confidence interval, what is the critical value for confidence level? (Give your answer to two decimal places.) zc = (a) Find an 80% confidence interval for the average weights of Allen's hummingbirds in the study region. What is the margin of error? (Round your answers to two decimal places.) lower limit upper limit margin of error (b) What conditions are necessary for your calculations? (Select all that apply.) σ is known σ is unknown uniform distribution of weights normal distribution of weights n is large (c) Interpret your results in the context of this problem. The probability that this interval contains the true average weight of Allen's hummingbirds is 0.80. The probability that this interval contains the true average weight of Allen's hummingbirds is 0.20. The probability to the true average weight of Allen's hummingbirds is equal to the sample mean. There is a 20% chance that the interval is one of the intervals containing the true average weight of Allen's hummingbirds in this region. There is an 80% chance that the interval is one of the intervals containing the true average weight of Allen's hummingbirds in this region. (d) Which equation is used to find the sample size n for estimating μ when σ is known? n = zσ E σ n = zσ σ E 2 n = zσ E σ 2 n = zσ σ E Find the sample size necessary for an 80% confidence level with a maximal margin of error E = 0.10 for the mean weights of the hummingbirds. (Round up to the nearest whole number.) hummingbirds

Here are summary statistics for randomly selected weights of newborn girls: n = 192, X=26.5 hg, S= 7.1 Construct a confidence interval estimate of the mean. Use a 99% confidence level. Are these results very different from the confidence interval 24.4 hg < U < 28.0 hg with only 19 sample values, X= 26.2 hg, and S= 2.7 Hg?

What is the confidence interval for the population mean ? ? ___hg < U< ___ hg

8. The following data are for a series of external standards of Cd²⁺ buffered to a pH of 4.6.¹⁴

[Cd²⁺] (nM) 15.4 30.4 44.9 59.0 72.7 86.0

S_spike (nA)    4.8 11.4 18.2    26.6    32.3    37.7

(a) Use a linear regression analysis to determine the equation for the calibration curve and report confidence intervals for the slope and the y-intercept.

(b) Construct a plot of the residuals and comment on their significance.

At a pH of 3.7 the following data were recorded for the same set of external standards.

[Cd²⁺] (nM) 15.4 30.4 44.9 59.0 72.7 86.0

S_spike (nA) 15.0    42.7 58.5 77.0 101    118

(c) How much more or less sensitive is this method at the lower pH?

(d) A single sample is buffered to a pH of 3.7 and analyzed for cadmium, yielding a signal of 66.3 nA. Report the concentration of Cd²⁺ in the sample and its 95% confidence interval.

An analysis is conducted to compare mean time to pain relief (measured in minutes) under four competing treatment regimens. Summary statistics on the four treatments are shown below. The ANOVA table presented below is not completed.

a. What is the within group (error) degrees of freedom value (df₂)?

b. Based on the data and ANOVA table provided in Q44, compute the MSE. (round to 2 decimal places)

c.  Based on the data and ANOVA table provided in Q44, compute the F test statistic. (round to 2 decimal places)

d.  What is the critical value for the hypothesis test you performed in Q44-Q46? (2 decimal places)

A small pilot study is conducted to investigate the effect of a nutritional supplement on total body weight. Six participants agree to take the nutritional supplement. To assess its effect on body weight, weights are measured before starting the supplementation and then after 6 weeks. The data are shown below. Is there a significant increase in body weight following supplementation? Run the test at a 5% level of significance, assuming the outcome is normally distributed. (enter 1 for “yes”, and 0 for “no”)