In the Focus Problem at the beginning of this chapter, a study was described comparing the hatch ratios of wood duck nesting boxes. Group I nesting boxes were well separated from each other and well hidden by available brush. There were a total of 469 eggs in group I boxes, of which a field count showed about 262 hatched. Group II nesting boxes were placed in highly visible locations and grouped closely together. There were a total of 804 eggs in group II boxes, of which a field count showed about 276 hatched.

(a) Find a point estimate p̂₁ for p₁, the proportion of eggs that hatch in group I nest box placements. (Round your answer to three decimal places.)
p̂₁ =

Find a 90% confidence interval for p₁. (Round your answers to three decimal places.)

(b) Find a point estimate p̂₂ for p₂, the proportion of eggs that hatch in group II nest box placements. (Round your answer to three decimal places.)
p̂₂ =

Find a 90% confidence interval for p₂. (Round your answers to three decimal places.)

(c) Find a 90% confidence interval for p₁ − p₂. (Round your answers to three decimal places.)

Does the interval indicate that the proportion of eggs hatched from group I nest boxes is higher than, lower than, or equal to the proportion of eggs hatched from group II nest boxes?

Because the interval contains only positive numbers, we can say that a higher proportion of eggs hatched in well-separated and well-hidden nesting boxes.Because the interval contains only negative numbers, we can say that a higher proportion of eggs hatched in highly visible, closely grouped nesting boxes.    We can not make any conclusions using this confidence interval.Because the interval contains both positive and negative numbers, we can not say that a higher proportion of eggs hatched in well-separated and well-hidden nesting boxes.

(d) What conclusions about placement of nest boxes can be drawn? In the article discussed in the Focus Problem, additional concerns are raised about the higher cost of placing and maintaining group I nest box placements. Also at issue is the cost efficiency per successful wood duck hatch.

A greater proportion of wood duck eggs hatch if the eggs are laid in highly visible, closely grouped nesting boxes.No conclusion can be made.    A greater proportion of wood duck eggs hatch if the eggs are laid in well-separated, well-hidden nesting boxes.The eggs hatch equally well in both conditions.

Edwards Manufacturing Company purchases two component parts from three different suppliers. The suppliers have limited capacity, and no one supplier can meet all the company’s needs. In addition, the suppliers charge different prices for the components. Component price data (in price per unit) are as follows:

Each supplier has a limited capacity in terms of the total number of components it can supply. However, as long as Edwards provides sufficient advance orders, each supplier can devote its capacity to component 1, component 2, or any combination of the two components, if the total number of units ordered is within its capacity. Supplier capacities are as follows:

If the Edwards production plan for the next period includes 1025 units of component 1 and 825 units of component 2, what purchases do you recommend? That is, how many units of each component should be ordered from each supplier? Round your answers to the nearest whole number. If your answer is zero, enter "0".

What is the total purchase cost for the components? Round your answer to the nearest dollar.

$__________

The distribution of weights for 12 month old baby girls in the US is approximately normal with mean u = 21 pounds and standard deviation of 2.2 pounds.

a) if a 12 month old girl weighs 23.2 pounds, approximately what weight percentile is she in?

b) if a 12 month old girl is in the 16th percentile in weight, estimate her weight.

c) Estimate the weight of t 12 month old girl who is in the 25th percentile by weight.

d) Estimate the weight of a 12 month old girl who is in the 75th percentile by weight.

Let X represent the weight of the students at a university. Suppose X has a mean of 75 kg and a standard deviation of 10 kg. Among 100 such randomly selected students from this university, what is the approximate probability that the average weight of this sample (X100) lies between

(a) 74 and 75 kg

(b) greater than 76 kg

(c) less than 73 kg

Assume that the sample size(N) is large enough for the CLT (Central Limit Theorem) to be applicable.

to pass a test you have to perform successfully two consecutive tasks, one easy and one hard. the easy task you think you can perform with probability z.and the hard task you think you can perform with probability h, where h<z. you are allowed three attempts. either in the order(easy, hard, easy)or in the order (hard, easy, hard). whichever order, you must be successful twice in a row to pas. assuming that your attempts are independent, in what order should you choose to talk to take the tasks in order to maximize your probability of passing the test?

Is there a way to do this without the binomial probability?

Consider the following game: You roll six 6-sided dice d1,…,d6 and you win if some number appears 3 or more times. For example, if you roll:

(3,3,5,4,6,6)

then you lose. If you roll

(4,1,3,6,4,4)then you win.

What is the probability that you win this game?

The answer is 119/324

The rare earth element gadolinium is often used as a contrasting agent for MRIs. The concentration of gadolinium was measured in the discharge from a wastewater treatment plant near a large medical facility. Eight measurements were obtained: 1.212001.21200 ppm, 1.212001.21200 ppm, 1.209001.20900 ppm, 1.203001.20300 ppm, 1.777001.77700 ppm, 1.201001.20100 ppm, 1.218001.21800 ppm, 1.201001.20100 ppm.

Use the Grubbs test to determine if one of these values is an outlier. What is the value of ?calcGcalc?

?calc=Gcalc=

Should this potential outlier be rejected with 95% confidence? Critical values of ?G can be found in this table.

The potential outlier should be rejected.

The potential outlier should be kept.

Based on the outcome of the Grubbs test, calculate the mean (?¯x¯), standard deviation (?s), and 99% confidence interval for the results. A list of ?t values can be found in the Student's ?t table.

?¯=x¯=

ppm

?=s=

ppm

confidence interval:?¯±x¯±

ppm

A Nielsen study indicates that 18-to-34 year olds spend a mean of 93 minutes whatching video on their smartphones per week. Assume that the amount of time watching video on a smartphone per week is normally distributed and that the standard deviation is 15 minutes.

1- What is the probability that an 18- to 34 year old spends less than 77 minutes watching video on his or her smartphone per week?

2- What is the probability that an 18- to 34- year old spends between 77 minutes and 109 minutes watching video on his or her smartphone per week?

3- What is the probability that an 18- to 34 year old spends more than 109 minutes watching video on his or her smartphone per week?

4- One percent of all 18- to 34- year olds will spend less than how many minutes watching video on his or her smartphone per week?

(Type it if possible)

To get published in an academic journal, you have to prove something "interesting." As a result, most academics begin their research by investigating hypotheses that, all else equal, are unlikely to be true. Suppose each research project begins with a research claim that has a 10% chance of being correct.

They then perform a study that satisfies the following two properties:

1) The probability that they correctly *find* an important result given that their *claim* is true is 50%
2) The probability that they incorrectly *find* an important result given that their *claim* is false is 5%

If they find an important result they are published. What is the probability that their claim was true, given that they were published?

In the college population, the mean reading comprehension test score is  μ = 75 and σ = 25. A researcher wanted to investigate the effect of listening to hip-hop music on reading comprehension. She randomly selected a sample of n = 100 college students. The sample of students completed a reading comprehension test while hip-hop music was played in the background the sample mean reading comprehension score was M = 68.

Do the data indicate a significant effect of hip-hop music on reading comprehension? Use a two-tailed z - test with p < .05  to answer this research question.

- Null and alternative hypotheses

- All computational steps of the z-test

- Critical z-value used for decision about H₀

- Decision about H₀ (i.e., reject or fail to reject)

- If the effect is significant, compute the Cohen's d to establish the size of the effect - is the effect small, medium or large?

- Conclusion in APA style: interpretation of the z-test outcome to answer the research question. Is there a significant effect of hip-hop music on reading comprehension or not? If there is a significant effect, address in your conclusion the direction of the effect (i.e., is the effect positive or negative/is there an improvement or decline of reading comprehension?) and report the Cohen's effect size.

Please explain in very broken down and simple steps, thank you!

Bhola Bhikhu is thinking about adding a new stock to her portfolio. Based on advice from a friend who claimed to make a lot of money, she decides to use the price to earnings ratio (P/E) as the only measurement of the performance of a stock. Bhola selects several possible stocks based on this measurement and will select one stock from the bundle. She assigns each of the selected stocks an equal chance of being selected. Stock one has a price to earnings ratio of 20, Stock two has an P/E of 22, Stock three has a P/E of 20, Stock four has a P/E of 18, and Stock five has a P/E of 16, and Stock six has a P/E of 20. Let ? denote the random variable representing the price to earnings ratio for the selected stock.

a) Create a PMF table for the random variable ?.

b) What is the probability that Bhola selects a stock with a P/E greater than 17?

c) Given that Bhola selects a stock with a P/E of at least 19, what is the probability that the P/E is over 20?

d) Given that Bhola selects a stock with a P/E greater than 17, what is the probability that the P/E is at most 22?

e) Find the expected value of ? and standard deviation of �

The National Sporting Goods Association (NSGA) conducted a survey of the ages of individuals that purchased skateboarding footwear. The ages of this survey are summarized in the following percent frequency distribution. Assume the survey was based on a sample of 200 individuals.

Calculate the mean and the standard deviation of the age of individuals that purchased skateboarding shoes. Use 10 as the midpoint of the first class. (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Mean-

Variance-

Standard Deviation-

Define a joint distribution for two random variables (X,Y) such that (i) Cov(X,Y)=0 and (ii) E[Y I X] is not equal to E[Y].

How do I define a joint distribution that satisfies both (i) and (ii) above at the same time?

Please give me an example and explanation of how it meets the two conditions.