Explain why the standard error of a sampling distribution will always be smaller than the standard deviation of a population. For you answer do not discuss the formula (since formulas are just the shorthand notation for concepts), explain this phenomenon conceptually.

A behavioral psychologist wanted to know if making a public commitment to lose weight will make a difference in how much weight is actually lost. He obtained 14 volunteers who wanted to lose weight and randomly assigned them to one of two groups. The “commitment” group met together and each participant stood and announced an intent to lose weight and signed a pledge to adhere to the diet and exercise regimen. The “control” was placed on the same diet and exercise regimen, but did not stand to announce their intent to lose weight and did not sign a pledge to adhere to the regimen. The commitment group participants lost 13, 11, 13, 12, 10, 9,and 8 pounds; the control group participants lost 10, 6, 7, 5, 9, 6, and 8 pounds. Did making a commitment to adhere to the diet and exercise regimen make a significant difference in weight loss?

• What is the IV? How many levels?
• What is the DV?
• Construct a frequency distribution with that data above for each group
• What are the means of the 2 groups?
• What is the df?
• What type of t test needs to be conducted?
• What is the calculated t statistic?
• Is this a one tail or 2 tail test?
• Are the findings significant at alpha .05? Explain what this means.

A random sample of medical files is used to estimate the proportion p of all people who have blood type B.

(a) If you have no preliminary estimate for p, how many medical files should you include in a random sample in order to be 85% sure that the point estimate p̂ will be within a distance of 0.06 from p? (Round your answer up to the nearest whole number.)
medical files

(b) Answer part (a) if you use the preliminary estimate that about 13 out of 90 people have blood type B.
medical files

A paper describes an investigation in which 40 men and 40 women with online dating profiles agreed to participate in a study. Each participant's height (in inches)was measured and the actual height was compared to the height given in that person's online profile. The differences between the online profile height and the actual height (profile − actual) were used to compute the values in the accompanying table.

For purposes of this exercise, assume it is reasonable to regard the two samples in this study as being representative of male online daters and female online daters. (Although the authors of the paper believed that their samples were representative of these populations, participants were volunteers recruited through newspaper advertisements, so we should be a bit hesitant to generalize results to all online daters.)

Use the paired t test to determine if there is convincing evidence that, on average, male online daters overstate their height in online dating profiles. Use

α = 0.05.

(Use a statistical computer package to calculate the P-value. Use μ_d = μ_profile − μ_actual. 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 =

(b)

Construct and interpret a 95% confidence interval for the difference between the mean online dating profile height and mean actual height for female online daters. (Use μ_d = μ_profile − μ_actual. Round your answers to two decimal places.)

____to___ inches

(c)

Use the two-sample t test of Section 11.1 to test H₀: μ_m − μ_f = 0 versus H_a: μ_m − μ_f > 0, where μ_m is the mean height difference (profile − actual) for male online daters and μ_f is the mean height difference (profile − actual) for female online daters. (Use α = 0.05. Use a statistical computer package to calculate the P-value. 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 the hypotheses, state the test statistic, state the P-value, make an decision, and state a conclusion.

A certain type of calculator battery has a mean lifetime of 150 hours and a standard deviation of of ? = 15 hours. A company has developed a new battery and claims it has a longer mean life. A random sample of 1000 batteries is tested, and their sample mean life is ?̅= 151.2 hours. Can you conclude that the new battery has a longer life? Use ? = 0.01.

3. Nelson's Foods wishes to compare the weight gain of infants using its brand versus their competitor's. A sample of 90 babies using Nelson's product revealed a mean weight gain of 7.6 pounds in the first three months. The population standard deviation for Nelson's brand was 2.3 pounds. A random sample of 105 babies using the competitor's brand revealed a mean weight gain of 8.2 pounds with a population standard deviation of 2.9 pounds. At the 6% significance level, can you conclude that babies using Nelson's brand gain less weight?

Consider the following:

H₀: μ=10
H₁: μ≠10

For a sample of 6 units, the mean for the sample is 11.2 and the population standard deviation is 2.14.

1)Calculate the p-value for the test.

2) If α=0.10, do you reject the null hypothesis?

A coffee company sells bags of coffee beans with an advertised weight of 454 grams. A random sample of 20 bags of coffee beans has an average weight of 457 grams. Weights of coffee beans per bag are known to follow a normal distribution with standard deviation 5 grams.

(a) Construct a 95% confidence interval for the true mean weight of all bags of coffee beans. (Instead of typing ±, simply type +-.) (1 mark)

(b) Provide an interpretation of the confidence interval in (a). (1 mark)

(c) Conduct a hypothesis test at the 5% level of significance to determine if there is evidence that the true mean weight of all bags of coffee beans differs from 454 grams. You will be marked on your calculation of the appropriate test statistic, P-value and a carefully worded conclusion.

(d) Provide an interpretation of the P-value in (c). (1 mark)

(e) Could the confidence interval in (a) have been used to conduct the test in (c)? Explain why or why not. If it could have been used, what would your conclusion be and why? (1 mark)

In January 2014, the “polar vortex” swept across the eastern US leading some media outlets to claim this was the “coldest weather in decades” in Baltimore between Jan 6 & Jan 8. It turns out that only 5 years prior, in 2009, Jan 15 – Jan 17 were 5 degrees colder in Baltimore than the coldest temperatures in 2014. Why did these media outlets say it was the “coldest weather in decades”? Many statisticians say that it is a mistake to look at weather temperature records the way that media outlets looked at the Baltimore "record"; why do you think they say this is a "mistake"?

The normaldistribution for women’s height in North America has a mean μ=62inches and a standard deviation ơ=2.75inches.The normal distribution for men’s height in North America has a mean μ=65inches and a standard deviation ơ=4 inches.Using the 68%, 95% and 99.7% Rule , determine in inches a). The women height interval fallingwithin 1standard deviation of the mean(Write the formula and show your work) b. The men height intervalfallingwithin 3standard deviation of the mean(Write the formula and show your work) c.(What percentage of the men heights falls between 57 inches and 73inches?(Write the formula and show your work)

The speed limit of a road is 65 miles per hour. The speed of a car on the highway follows a normal distribution with a mean of 70 and standard deviation of 5. What percent of the distribution breaks the speed limit?

The speed limit of a road is 65 miles per hour. The speed of a car on the highway follows a normal distribution with a mean of 70 and standard deviation of 5. A police officer will only react to speeding if the person is going 3 standard deviations above the average (z = 3). What is the speed at which he will react?

• Alabama 89.3%
• Alaska 78.2%
• Arizona 78%
• Arkansas 88%
• California 82.7%
• Colorado 79.1%
• Connecticut 87.9%
• Delaware 86.9%
• Florida 82.3%
• Georgia 80.6%
• Hawaii 82.7%
• Idaho 79.7%
• Illinois 87%
• Indiana 83.8%
• Iowa 91%
• Kansas 86.5%
• Kentucky 89.7%
• Louisiana 78.1%
• Maine 86.9%
• Maryland 87.7%
• Massachusetts 88.3%
• Michigan 80.2%
• Minnesota 82.7%
• Mississippi 83%
• Missouri 88.3%
• Montana 85.8%
• Nebraska 89.1%
• Nevada 80.9%
• New Hampshire 88.9%
• New Jersey 90.5%
• New Mexico 71.1%
• New York 81.8%
• North Carolina 86.6%
• North Dakota 87.2%
• Ohio 84.2%
• Oklahoma 82.6%
• Oregon 76.7%
• Pennsylvania 86.6%
• Rhode Island 84.1%
• South Carolina 83.6%
• South Dakota 83.7%
• Tennessee 89.8%
• Texas 89.7%
• Utah 86%
• Vermont 89.1%
• Virginia 86.9%
• Washington 79.4%
• West Virginia 89.4%
• Wisconsin 88.6%
• Wyoming 86.2%
• THESE ARE GRADUATION RATES FOR EACH OF THE 50 states. Here are the instructions:
• ample Data—Include a 5x10 table including your 50 values in your report. You must provide ALL of your sample data.
• Problem Computations—For the topic you chose, you must answer the following:
• Determine the mean and standard deviation of your sample.
• Find the 80%, 95%, and 99% confidence intervals.
• Make sure to list the margin of error for the 80%, 95%, and 99% confidence interval.
• Create your own confidence interval (you cannot use 80%, 95%, and 99%) and make sure to show your work. Make sure to list the margin of error.

A study conducted by the Pew Research Center reported that 58% of cell phone owners used their phones inside a store for guidance on purchasing decisions. A sample of 15 cell phone owners is studied. Would it be unusual if more than 12 of them had used their phones for guidance on purchasing decisions?

Find the sample size needed to estimate the percentage of Virginia residents who are left-handed. Use a Margin of Error of 3% and use a confidence level of 90% for both situations as follows.

a. Assume phat is unknown

b. Based on prior studies, use phat= 12%

Recall from Example 1 that whenever Suzan sees a bag of marbles, she grabs a handful at random. She has seen a bag containing four red marbles, two green ones, five white ones, and one purple one. She grabs eight of them. Find the probability of the following event, expressing it as a fraction in lowest terms. HINT [See Example 1.]

She has at least one green one.