The data from Exhibit 3 is also in the Excel file income.xls on the course website. Use Excel, along with this file, to determine Mrs. Bella’s real income for the last fifteen years. Do this by first converting each price index from percent by dividing by 100. Then, divide gross income by your converted (adjusted) price index. Using Excel, find the mean, median, standard deviation, and variance of her past real income. Explain the meaning of these statistics. Can you use mean income to forecast future earnings? Take into account both statistical and non-statistical considerations.

1. Each month, the owner of Fay's Tanning Salon records in a data file the monthly total sales receipts and the amount spend that month on advertising. (a) Identify the two variables. (b) For each variable, indicate whether it is quantitative or categorical. (c) Identify the response variable and the explanatory variable.

At a Bloomburg City Council meeting, a plan to fund more swim safety programs was presented. The reasoning behind the request was that less than 40% of children under the age of 5 could pass a swim test. If this is true, the council will agree to fund more programs for these kids. The council decides to take a 200-person volunteer sample of children under 5 years in Bloomburg City and conduct a significance test for H0: p = 0.40 and Ha: p < 0.40, where p is the proportion of these children that can pass a swim test. They will perform a significance test at a significance level of α = 0.05 for the hypotheses.

Part A: Describe a Type II error that could occur. What impact could this error have on the situation?

Part B: Out of the 200 children under 5 that volunteered to take a swimming test, 87 passed, resulting in a p-value of 0.8438. What can you conclude from this p-value given the data of the 200 children is sufficient to perform a significance test for the hypotheses?

Part C: What possible defect in the study can you find in Part B? Explain.

The mean and standard deviation for the diameter of a certain type of steel rod are mu = 0.503 cm and sigma = 0.03cm. Let X denote the average of the diameters of a batch of 100 such steel rods. The batch passes inspection if Xbar falls between 0.495 and 0.505cm.

1. What is the approximate distribution of Xbar? Specify the mean and the variance and cite the appropriate theorem to justify your answer.

2. What is the approximate probability the batch will pass inspection?

3. Over the next six months 40 batches of 100 will be delivered. Let Y denote the number of batches that will pass inspection.

(a) the distribution of Y is: Binomial, hypergeometric, negative binomial, OR poisson?

(b) give the approximation, as accurately as possible, to the probability P(Y ≤ 30).

Use the Voltage data to test the claim that home voltages and generator voltages are from populations with the same mean.

1. Create a histogram on the difference in voltage between home voltage and generator voltage. Copy and paste your histogram here.

2. Does our assumption of normality appear to be satisfied?
   1. Yes
   2. No

3. What is your null and alternative?
   1. H0: µ1 = µ2, H1: µ1 ≠ µ2
   2. H0: µ1 ≠ µ2, H1: µ1 = µ2
   3. H0: µ1 = µ2, H1: µ1 > µ2
   4. H0: µ1 > µ2, H1: µ1 = µ2
   5. None of the abov Provide your own answer.

4. What is your decision?
   1. Support H1
   2. Cannot support H1
   3. Cannot make a decision at this time
   4. We do not have enough data to make an educated guess
   5. None of the abov Provide your own answer.

5. What is your conclusion?
   1. We have sufficient evidence to show that the mean voltage is the same for home voltage and generator voltage.
   2. We do not have sufficient evidence to show that the mean voltage is the same for home voltage and generator voltage.
   3. We have sufficient evidence to show the mean voltage is the higher for home voltage than generator voltage.
   4. We do not have sufficient evidence to show that the mean voltage is the higher for home voltage than generator voltage.
   5. None of the abov Provide your own answer.

6. Does the confidence interval support your conclusion?
   1. Yes
   2. No
   3. Cannot determine at this time
   4. None of the above. Provide your own answer.

7. If there is a statically significant difference, does that difference have practical significance?
   1. Yes
   2. No

Home   Generator
123.8   124.8
123.9   124.3
123.9   125.2
123.3   124.5
123.4   125.1
123.3   124.8
123.3   125.1
123.6   125.0
123.5   124.8
123.5   124.7
123.5   124.5
123.7   125.2
123.6   124.4
123.7   124.7
123.9   124.9
124.0   124.5
124.2   124.8
123.9   124.8
123.8   124.5
123.8   124.6
124.0   125.0
123.9   124.7
123.6   124.9
123.5   124.9
123.4   124.7
123.4   124.2
123.4   124.7
123.4   124.8
123.3   124.4
123.3   124.6
123.5   124.4
123.6   124.0
123.8   124.7
123.9   124.4
123.9   124.6
123.8   124.6
123.9   124.6
123.7   124.8
123.8   124.3
123.8   124.0

Another medical student named Emily is also studying the population of pregnant women in the United States, and is also interested in the duration of their pregnancies (in days). Emily will compute a 95% confidence interval. Like Sheena, Emily knows that the population standard deviation equals 16 days. Emily takes a random sample of 20 pregnant women (this is a different random sample than Sheena's!). The sample mean duration among the 20 pregnancies in Emily's sample equals 278. Emily's 95% confidence interval equals ( A, B ). What is the value of B? Round off to the second decimal place.

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Question 71 pts

Suppose Emily decided that the error margin of her 95% confidence interval was too large and wanted an error margin of 1.7 days while maintaining a 95% confidence level. She should take another random sample of size n = _________. (Remember to always round sample sizes up to the next integer.)

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Question 81 pts

If Emily had used the same data to compute a 99% confidence interval (instead of a 95% confidence interval), it would have been _________.

Group of answer choices

the same width

wider

thinner

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Question 91 pts

For both Sheena’s hypothesis test and Emily's confidence interval, what is statement is true?

Group of answer choices

Since the sample size is large, they are NOT required to assume the population is normally distributed.

Since the sample size is large, they ARE required to assume the population is normally distributed.

Since the sample size is small, they are NOT required to assume the population is normally distributed.

Since the sample size is small, they ARE required to assume the population is normally distributed.

We want to examine the efficacy of the current flu vaccine at preventing the flu. Once flu season is over we ask 500 people if they got the vaccine and if they contracted the flu. We then break them into groups (those who got the vaccine and those who did not) and compare them based upon whether or not they contracted the flu.

Suppose your test statistic is statistically significant. Interpret what this significant result means in terms of the alpha and p-value AND what would you conclude about the null hypothesis for this particular research (retain or reject and state in words the conclusion you would draw about the relationship between the two variables).

The amount of corn chips dispensed into a 10-ounce bag by the dispensing machine has been identified at possessing a normal distribution with a mean of 10.5 ounces and a standard deviation of 0.2 ounces (these are the population parameters). Suppose a sample of 100 bags of chips were randomly selected from this dispensing machine. Find the probability that the sample mean weight of these 100 bags exceeded 10.6 ounces. (Hint: think of this in terms of a sampling distribution with sample size = 100)

Chapter 7 hand-in Homework
1) Mention three thing about the standard error of the mean

2) Why is the Central Limit Theorem important in statistics?

3) The diameter of a brand of tennis balls is approximately normally distributed, with a mean of 2.63 inches and a standard deviation of 0.03 inch. If you select a random sample of nine tennis balls, 
a) What is the sampling distribution of the mean?   

b) Assume the diameter of a brand of tennis balls was known to have a right skewed distribution with a mean of 2.63 inches and a standard deviation of 0.03 inch. Suppose we collect a random sample of 100 tennis balls. Describe the sampling distribution of the mean diameter for these 100 tennis balls.

c) How will the mean of the sampling distribution compare to the population mean in this problem?

d) How will the standard deviation of the sampling distribution (standard error of the mean) compare to the population standard deviation?

e) Find the approximate probability that the mean diameter of nine tennis balls exceeded 2.61.

f) Find the approximate probability that the mean diameter of the nine tennis balls exceeded 2.68.

g) Find the approximate probability that the mean diameter of the nine tennis balls was no more than 2.60 inches.

4) n a random sample of 64 people, 48 are classified as “successful”.
a) Determine the sample proportion, p, of “successful” people.

b) Determine the standard error of the proportion.

c) What proportion of the samples will have between 20% and 30% of people who will considered “successful”?

d) What proportion of the samples will have less than 75% of people who will be considered “successful”?

e) 90% of the samples will have less than what percentage of people who will be considered “successful”?

f) 90% of the samples will have more than what percentage of people who will be considered “successful”?

A team of visiting polio eradication workers were informed during their orientation session that population-wide studies done in their host country showed that the risk of polio in villages of that country was strongly epidemiologically associated with the village’s economic/human development circumstances, which ranged greatly from village to village.  In some villages, residents lived in hand-constructed huts with no running water, no latrines or sewage disposal areas, and no electricity.  In other places, residents lived in wooden or adobe homes which, though modest by Western standards, had all of the above services in place and whose street side craft shops and food markets did a brisk business, catering both to locals and visitors.

Knowing this information, the team went into several villages and attempted to assign a “human development rating” to each family. This was based on that family’s income situation, access to running water, access to elementary school for their children, and the condition of the home. To their surprise, they found that families in all the villages had no difference in polio risk based on the family’s human development rating.

The following table shows a portion of the monthly returns data (in percent) for 2010–2016 for two of Vanguard’s mutual funds: the Vanguard Energy Fund and the Vanguard Healthcare Fund. [You may find it useful to reference the t table.]

H₀: ρ_xy = 0; H_A: ρ_xy ≠ 0b. Specify the competing hypotheses in order to determine whether the population correlation coefficient is different from zero.

H₀: ρ_xy ≤ 0; H_A: ρ_xy > 0

H₀: ρ_xy ≥ 0; H_A: ρ_xy < 0

c-1. Calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.)

c-2. Find the p-value.

p-value < 0.01

0.01 ≤ p-value < 0.02

0.02 ≤ p-value < 0.05

0.05 ≤ p-value < 0.10

p-value ≥ 0.10

MORE BENEFITS OF EATING ORGANIC

Using specific data, 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. 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. Use a 5% significance level.

Effect of Organic Potatoes After 11 Days

After 11 days, the proportion of fruit flies eating organic potatoes still alive is 0.69 , while the proportion still alive eating conventional potatoes is 0.66 . The standard error for the difference in proportions is 0.031 .

What is the value of the test statistic?

Round your answer to two decimal places.

 z= 

What is the p-value?

Round your answer to three decimal places.

p-value = Enter your answer; p-value

What is the conclusion?

Choose the answer from the menu;                                                          Reject H_0.Do not reject H_0.

Is there evidence of a difference?

Choose the answer from the menu; Is there evidence of a difference?                                                          YesNo

A physician wants to develop criteria for determining whether a​ patient's pulse rate is​ atypical, and she wants to determine whether there are significant differences between males and females. Use the sample pulse rates below.
Male
96
84
68
76
68
60
60
60
84
88

Female
104
88
72
84
84
72
64
60
76
124

Assume that females have pulse rates that are normally distributed with a mean of mu equals 73.0 beats per minute and a standard deviation of sigma equals 12.5 beats per minute. Complete parts​ (a) through​ (c) below. a. If 1 adult female is randomly​ selected, find the probability that her pulse rate is less than 79 beats per minute. The probability is ___. ​(Round to four decimal places as​ needed.) b. If 4 adult females are randomly​ selected, find the probability that they have pulse rates with a mean less than 79 beats per minute. The probability is ___ ​(Round to four decimal places as​ needed.)

c. Why can the normal distribution be used in part​ (b), even though the sample size does not exceed​ 30?

A. Since the original population has a normal​ distribution, the distribution of sample means is a normal distribution for any sample size.

B. Since the distribution is of​ individuals, not sample​ means, the distribution is a normal distribution for any sample size.

C. Since the mean pulse rate exceeds​ 30, the distribution of sample means is a normal distribution for any sample size.

D. Since the distribution is of sample​ means, not​ individuals, the distribution is a normal distribution for any sample size.

In a study of the domestic market share of the three major automobile manufacturers A, B, and C in a certain country, it was found that their current market shares were 60%, 20%, and 20%, respectively. Furthermore, it was found that of the customers who bought a car manufactured by A, 75% would again buy a car manufactured by A, 15% would buy a car manufactured by B, and 10% would buy a car manufactured by C. Of the customers who bought a car manufactured by B, 90% would again buy a car manufactured by B, whereas 5% each would buy cars manufactured by A and C. Finally, of the customers who bought a car manufactured by C, 85% would again buy a car manufactured by C, 5% would buy a car manufactured by A, and 10% would buy a car manufactured by B. Assuming that these sentiments reflect the buying habits of customers in the future, determine the market share that will be held by each manufacturer after the next two model years. (Round your answers to the nearest percent.)