Can you show how to draw the normal curve for each of the problems and label it as well?

Heights of MEN in the U.S. are normally distributed µ = 69.6 inches with σ = 3 inches.

-________ percent (to nearest %) of men in the U.S. are either shorter than 5 ft. or taller than 6 ft?

-In a group of 150 U.S. men, approximately ________ of them should be shorter than 65 inches.

-A male height of _______________ corresponds to the 58th percentile in the U.S. population. -_______________ is the cutoff height to be in the top 12% of male heights in the U.S.

-The middle 72% of U.S. men will be between ________ inches and ________ inches tall. -A man in the U.S. shorter than ___________ inches would be considered "unusually short. ( Can you Show your work or explain answer.)

Find the mean, median, and mode for the scores in the following frequency distribution table:

The mean (to two decimal places) is   , the median is   , and the mode is   .

Based on the three values for central tendency, what is the most likely shape for this distribution of scores?

The distribution is    because the mean is   the median and the median is      the mode.

The Downtown Parking Authority of Tampa, Florida, reported the following information for a sample of 231 customers on the number of hours cars are parked and the amount they are charged.

Use the data set below to answer the question.

Find a 90% prediction interval for some value of y to be observed in the future when

x = −1.

(Round your answers to three decimal places.)

4. The Pew Research Center conducted a survey in 2019 asking U.S. adults about their experiences dating online. In a random sample of 100 adults who had dated online, 25 said dating sites made them feel insecure. Research question: Is the amount of online daters who believe dating sites make them feel insecure different than a third?

a. Compute the value of the statistic.

b. What are the hypothesis statements to answer the research question?

c. Are the appropriate conditions met to conduct a hypothesis test using the standard normal distribution? Explain.

d. Compute the value of the test statistic.

e. Find p-value using the appropriate theoretical distribution in StatKey (include screenshot from StatKey): p-value =

f. What is your conclusion in the context of this study?

A Californian Chenin Blanc was evaluated on a 9-pt scale representing varietal nature (with 1=very dissimilar and 9=very similar in varietal nature). Permission was sought for a Jamaican wine made from Chenin Blanc grapes grown in Jamaica to also be called “Chenin Blanc.” It was decided that if the “varietal nature” scores of the Jamaican wine (as assigned by 8 experts) were not significantly different from the California Chenin Blanc scores, permission will be given. (8 pts)

Question 1: What is the value of S?

Question 2: What is the critical value of t? This is the value from the table.

Question 3: What is the calculated t-value?

Question 4: Are there significant differences between the wines? State this in terms of the relationship between calculated t-value and critical t-value. (2 pts)

Question 5: Can this Jamaican wine be called “Chenin Blanc?” Look back to the question above and state the p-value in the response. (2 pts)

Question 6: Would using more experts provide a more robust conclusion? Why or why not?

A statistical program is recommended.

The National Football League (NFL) records a variety of performance data for individuals and teams. To investigate the importance of passing on the percentage of games won by a team, the following data show the conference (Conf), average number of passing yards per attempt (Yds/Att), the number of interceptions thrown per attempt (Int/Att), and the percentage of games won (Win%) for a random sample of 16 NFL teams for one full season.

(c)

Develop the estimated regression equation that could be used to predict the percentage of games won given the average number of passing yards per attempt and the number of interceptions thrown per attempt. (Round your numerical values to the nearest integer. Let x₁ represent Yds/Att, x₂ represent Int/Att, and y represent Win%.)

ŷ =

(d)

The average number of passing yards per attempt for a certain team was 6.2 and the number of interceptions thrown per attempt was 0.038. Use the estimated regression equation developed in part (c) to predict the percentage of games won by the team. (Round your answer to one decimal place.)

.

A yield improvement study at a semiconductor manufacturing facility provided defect data for a sample of 450 wafers. The following table presents a summary of the responses to two questions” Were particles found on the die that produced the wafer?” and “is the wafer good or bad?”

1. Suppose you know that a wafer is bad. What then is the probability that it was produced from a die that had particles?
2. Suppose you know that a wafer is good. What then is the probability that it was produced from a die that had particles?
3. Are the two events, a good wafer and a die with no particles, statistically independent? Explain.

Show working

A study of iron deficiency among infants compared samples of infants following different feeding regimens. One group contained breast-fed infants, while the infants in another group were fed a standard baby formula without any iron supplements. Here are summary results on blood hemoglobin levels at 12 months of age.

(a)

Is there significant evidence that the mean hemoglobin level is higher among breast-fed babies? State H₀ and H_a.

H₀: μ_breast-fed > μ_formula;   H_a: μ_breast-fed = μ_formula

H₀: μ_breast-fed < μ_formula;   H_a: μ_breast-fed = μ_formula     

H₀: μ_breast-fed ≠ μ_formula;   H_a: μ_breast-fed < μ_formula

H₀: μ_breast-fed = μ_formula;   H_a: μ_breast-fed > μ_formula

Carry out a t test. Give the P-value. (Use α = 0.01. Use μ_breast-fed − μ_formula. Round your value for t to three decimal places, and round your P-value to four decimal places.)

t = _______

P-Value = _______

What is your conclusion?

Fail to reject the null hypothesis. There is significant evidence that the mean hemoglobin level is higher among breast-fed babies.

Reject the null hypothesis. There is significant evidence that the mean hemoglobin level is higher among breast-fed babies.     

Fail to reject the null hypothesis. There is not significant evidence that the mean hemoglobin level is higher among breast-fed babies.

Reject the null hypothesis. There is not significant evidence that the mean hemoglobin level is higher among breast-fed babies.

(b)

Give a 95% confidence interval for the mean difference in hemoglobin level between the two populations of infants. (Round your answers to three decimal places.)

( _______, _______ )

(c)

State the assumptions that your procedures in (a) and (b) require in order to be valid.

We need sample sizes greater than 40.

We need two independent SRSs from normal populations.     

We need two dependent SRSs from normal populations.

We need the data to be from a skewed distribution.

Please evaluate the correlation matrix below, assuming stock price is the response variable in a series of multiple regression equations you plan to run. If you are using this as a diagnostic tool, what are you looking for? If this was your data, how would you proceed?

Given 2 trains per hour and passengers arrive according to a triangular distribution of waiting times with mode of 5 minutes.

a) What is the expected wait time?

b) What is the probability that a random passenger will wait less than 5 minutes?

C) What is the probability that a random passenger will wait less than 10 minutes?

please show steps for the solution.

When σ is unknown and the sample is of size n ≥ 30, there are two methods for computing confidence intervals for μ.

Method 1: Use the Student's t distribution with d.f. = n − 1.
This is the method used in the text. It is widely employed in statistical studies. Also, most statistical software packages use this method.
Method 2: When n ≥ 30, use the sample standard deviation s as an estimate for σ, and then use the standard normal distribution.
This method is based on the fact that for large samples, s is a fairly good approximation for σ. Also, for large n, the critical values for the Student's t distribution approach those of the standard normal distribution.

Consider a random sample of size n = 36, with sample mean x = 44.0 and sample standard deviation s = 6.1.

(a) Compute 90%, 95%, and 99% confidence intervals for μ using Method 1 with a Student's t distribution. Round endpoints to two digits after the decimal.

(b) Compute 90%, 95%, and 99% confidence intervals for μ using Method 2 with the standard normal distribution. Use s as an estimate for σ. Round endpoints to two digits after the decimal.

(d) Now consider a sample size of 71. Compute 90%, 95%, and 99% confidence intervals for μ using Method 1 with a Student's t distribution. Round endpoints to two digits after the decimal.

(e) Compute 90%, 95%, and 99% confidence intervals for μ using Method 2 with the standard normal distribution. Use s as an estimate for σ. Round endpoints to two digits after the decimal.

(f) Compare intervals for the two methods. Would you say that confidence intervals using a Student's t distribution are more conservative in the sense that they tend to be longer than intervals based on the standard normal distribution?

MORE BENEFITS OF EATING ORGANIC

Using data from a study, we find a significant difference in the proportion of fruit flies surviving after 13 days between those eating organic potatoes and those eating conventional (not organic) potatoes. This exercise asks you to conduct a hypothesis test using additional data from this study.¹ In this case, we are testing

H0:po=pcHa:po>pc

where po and pc represent the proportion of fruit flies alive at the end of the given time frame of those eating organic food and those eating conventional food, respectively. We have n1=n2=500. Show all remaining details in the test, using a 5% significance level.

Effect of Organic Raisins After 20 Days

After 20 days, 275 of the 500 fruit flies eating organic raisins are still alive, while 170 of the 500 eating conventional raisins are still alive.


¹Proportions approximated from information given in the paper.

Give the test statistic and the p-value.

Round your answers to three decimal places.

Test statistic = Enter your answer; test statistic

p-value =

Listed below are the data for a local radio station. This shows the number of weekly radio advertisements and the projected weekly sales resulting (adjusted by industry). Weekly Radio Spots Sales

a. Show the data in a scatterplot, to demonstrate the relationship between the two variables.

b. Compute and interpret the correlation coefficient.