3). You are given the claim that the mean of a population is not equal to 24 cm. You
don’t believe in this claim and so you want to test it. Suppose that you know the
population standard deviation is 4 cm, and the population distribution is approximately
normal. To test this claim, you take a random sample as follows
X = (20, 23, 22, 24, 24, 24, 25, 26, 24, 23, 27, 24, 29, 20, 25, 26, 28).
Is there enough evidence to support the claim? Justify your answer completely.

4) Based on problem 3 above, compute the 95 % confidence interval of the true mean.
Interpret this confidence interval and also explain what is the meaning of the 95%
confidence level.

A simple random sample from a population with a normal distribution of

9797

body temperatures has

x overbarxequals=98.7098.70degrees Upper F°F

and

sequals=0.670.67degrees Upper F°F.

Construct

a

99​%

confidence interval estimate of the standard deviation of body temperature of all healthy humans.

Potatoes - Samples: Suppose the weights of Farmer Carl's potatoes are normally distributed with a mean of 8.0 ounces and a standard deviation of 1.3 ounces.

Suppose Carl bags his potatoes in randomly selected groups of 6. What percentage of these bags should have a mean potato weight between 7.5 and 8.5 ounces? Enter your answer as a percentage rounded to one decimal place.
%

Listed below are the weights (in grams) of a sample of M&M's Plain candies, classified according to color.

1. Identify the null hypothesis and the alternate hypothesis.

Null hypothesis:

a) H₀: μ₁ ≠ μ₂ ≠ μ₃ ≠ μ₄ ≠ μ₅ ≠ μ₆

b) H₀: μ₁ = μ₂ = μ₃ = μ₄ = μ₅ = μ

2. Alternate hypothesis:

• The treatment means are equal.

• Not all treatment means are equal.

3. State the decision rule for 0.05 significance level. (Round your answer to 2 decimal places.

4. Complete the ANOVA table. (Round your SS, MS to 3 decimal places, and F to 3 decimal places.)

5. Use a statistical software system to determine whether there is a difference in the mean weights of candies of different colors. Use the 0.05 significance level.

List three types of regression and a real-world example of each. Why do you think regression is so critical in statistics?

A random sample of 150 men found that 88 of the men exercise regularly, while a random sample of 200 women found that 130 of the women exercise regularly.

a. Based on the results, construct and interpret a 95% confidence interval for the difference in the proportions of women and men who exercise regularly.

b. A friend says that she believes that a higher proportion of women than men exercise regularly. Does your confidence interval support this conclusion? Explain.

Allen's hummingbird (Selasphorus sasin) has been studied by zoologist Bill Alther.† Suppose a small group of 17 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 = 0.40 gram.

(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.)

(b) What conditions are necessary for your calculations? (Select all that apply.)

σ is unknownn is large

σ is known normal

distribution of weights

uniform distribution of weights

(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 0.20.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.    The probability that this interval contains the true average weight of Allen's hummingbirds is 0.80.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.

(d) Find the sample size necessary for an 80% confidence level with a maximal margin of error E = 0.16 for the mean weights of the hummingbirds. (Round up to the nearest whole number.)
hummingbirds

1. A researcher wants to know what kind of exercising is most likely to lead to improve people’s moods. He has participants engage in one month of regular workouts (cardio, weight training, or yoga) and then has them complete a mood measure (1-10, higher scores = better mood). Is there a significant difference in groups? Hand calculate the ANOVA using a significance level of .05 and then check your work using SPSS.

Hypothesis:

F_crit /threshold:

Conclusion:

An experiment was conducted to determine if there was a mean difference in weight for women based on type of aerobics exercise program participated (low impact vs. high impact). Body mass index (BMI) was used as a blocking variable to represent below, at, or above recommended BMI. The data are shown as follows. Conduct a two-factor randomized block ANOVA (alpha = .05) and Bonferroni MCPs using SPSS to determine the results of this study.

Two brands of car​ batteries, both carrying​ 6-year warranties, were sampled and tested under controlled conditions. Five of each brand failed after the number of months shown. Calculate ​a) both sample means and ​b) both sample standard deviations. Decide ​c) which brand battery lasts longer and ​d) which brand has the more consistent lifetime. Brand​ A: 68​, 69​, 76​, 76​, 73 Brand​ B: 61​, 69​, 68​, 67​, 61

What are the sample​ means?A B

What are the sample standard​ deviations? SA SB

Which brand battery apparently lasts​ longer?BRAND A OR B

Which brand battery has the more consistent​ lifetime?BRAND A OR B

The scores of students on the SAT college entrance examinations at a certain high school had a normal distribution with mean μ=542.7 and standard deviation σ=29.8.

(a) What is the probability that a single student randomly chosen from all those taking the test scores 546 or higher?
ANSWER:  

For parts (b) through (d), consider a simple random sample (SRS) of 35 students who took the test.

(b) What are the mean and standard deviation of the sample mean score x¯, of 35 students?
The mean of the sampling distribution for x¯is:  
The standard deviation of the sampling distribution for x¯ is:

(c) What z-score corresponds to the mean score x¯ of 546?
ANSWER:

(d) What is the probability that the mean score x¯ of these students is 546 or higher?
ANSWER:  

Since an instant replay system for tennis was introduced at a major​ tournament, men challenged 1427 referee​ calls, with the result that 411 of the calls were overturned. Women challenged 747 referee​ calls, and 215 of the calls were overturned. Use a 0.01 significance level to test the claim that men and women have equal success in challenging calls. Complete parts​ (a) through​ (c) below. a. Test the claim using a hypothesis test. Consider the first sample to be the sample of male tennis players who challenged referee calls and the second sample to be the sample of female tennis players who challenged referee calls. What are the null and alternative hypotheses for the hypothesis​ test?

Identify the test statistic.

z=?

​(Round to two decimal places as​ needed.)

Identify the​ P-value.

​P-value=?

​(Round to three decimal places as​ needed.)

What is the conclusion based on the hypothesis​ test?

The​ P-value is greater than or less than ?

the significance level of alpha equals 0.01​, so

reject or fail to reject ? the null hypothesis.

There is sufficient or is not sufficient ?

evidence to warrant rejection of the claim that women and men have equal success in challenging calls.

b. Test the claim by constructing an appropriate confidence interval.

The 99% confidence interval is ?

? < (p 1 - p 2)< ?

.

​(Round to three decimal places as​ needed.)

What is the conclusion based on the confidence​ interval?

Because the confidence interval limits include or do not include? 0,

there does not or does ?

appear to be a significant difference between the two proportions.

There is not sufficient or is sufficient? evidence to warrant rejection of the claim that men and women have equal success in challenging calls.

c. Based on the​ results, does it appear that men and women may have equal success in challenging​ calls?

A. The confidence interval suggests that there is a significant difference between the success of men and women in challenging calls. It is reasonable to speculate that men have more success.

B. The confidence interval suggests that there is no significant difference between the success of men and women in challenging calls.

C. The confidence interval suggests that there is a significant difference between the success of men and women in challenging calls. It is reasonable to speculate that women have more success.

D. There is not enough information to reach a conclusion.

a study of prostate cancer was initiated in Des Moines, Iowa. A total of 1,000 men, 55-64 years of age, with no prior evidence of prostate cancer were enrolled in the study. Each year during the study, the men being observed were examined and tested for the presence of prostate cancer. The results of the annual exam revealed: 10 cases confirmed at the 1st exam, 15 additional cases at 2nd exam, 20 additional cases at 3rd exam, 25 additional cases at the 4th exam. What is the incidence density of prostate cancer in the group?

The results indicated that more money was donated in the identified-victim-only condition than in the statistics-only condition (p = .02). Compute the t_LSD value here.

For low Rational scorers,

donations differed significantly by request type, F(2, 55) = 3.35, p < .05,

η² = .109, MSE. 2.98. In planned comparisons based on Small et al.’s

findings (2007, Study 3), donations were higher when a personalized victim

appeared alone (M = $3.18, n =17) than when statistics were added to the

victim request (M = $2.00, n = 22, p = .04) or when statistics were presented

alone (M = $1.79, n = 19, p = .02). The latter two means did not differ.

1. The U.S. Department of Transportation reported that during November, 83.4% of Southwest
Airlines’ flights, 75.1% of US Airways’ flights, and 70.1% of JetBlue’s flights arrived on time (USA
Today, January 4, 2007). Assume that this on-time performance is applicable for flights arriving at
concourse A of the Rochester International Airport, and that 40% of the arrivals at concourse Aare
Southwest Airlines flights, 35% are US Airways flights, and 25% are JetBlue flights.
a. An announcement has just been made that Flight 1424 will be arriving at gate in concourse A.
What is the most likely airline for this arrival?
c. What is the probability that Flight 1424 will arrive on time?
d. Suppose that an announcement is made saying that Flight 1424 will be arriving late. What is the
most likely airline for this arrival? What is the least likely airline?

2. In San Francisco, 30% of workers take public transportation daily (USA Today, December 21, 2005).
a. In a sample of 10 workers, what is the probability that exactly three workers take public
transportation daily?
b. In a sample of 10 workers, what is the probability that at least three workers take public
transportation daily?

3. Auniversity found that 20% of its students withdraw without completing the introductory statistics
course. Assume that 20 students registered for the course.
a. Compute the probability that two or fewer will withdraw.
b. Compute the probability that exactly four will withdraw.
c. Compute the probability that more than three will withdraw.
d. Compute the expected number of withdrawals.

4. Phone calls arrive at the rate of 48 per hour at the reservation desk for Regional Airways.
a. Compute the probability of receiving three calls in a 5-minute interval of time.
b. Compute the probability of receiving exactly 10 calls in 15 minutes

.
5. More than 50 million guests stay at bed and breakfasts (B&Bs) each year. The website for the Bed
and Breakfast Inns of North America, which averages seven visitors per minute, enables many
B&Bs to attract guests (Time, September 2001).
a. Compute the probability of no website visitors in a one-minute period.
b. Compute the probability of two or more website visitors in a one-minute period.

6. In a survey conducted by the Gallup Organization, respondents were asked, “What is your favorite
sport to watch?” Football and basketball ranked number one and two in terms of preference
(Gallup website, January 3, 2004). Assume that in a group of 10 individuals, seven prefer football
and three prefer basketball. A random sample of three of these individuals is selected.
a. What is the probability that exactly two prefer football?
b. What is the probability that the majority (either two or three) prefer football?