The time married men with children spend on child care averages 6.4 hours per week {Time, March 12, 2012). You belong lo a professional group on family practices that would like to do its own study to determine if the time married men in your area spend on child care per week differs from the reported mean of 6.4 hours per week. A sample of 40 married couples will be used with the data collected showing the hours per week the husband spends on child care.

Use the sample data to perform a t-test to determine if the population mean number of hours married men are spending in child care differs from the mean reported by Time in your area? Use α = 0.05 as the level of significance.

1.

1. Whats the null and alternative hypothesis, what type of test is it?

2. Compute,

3. Do you reject or fail to reject the null hypothesis. Explain why. Use the α = 0.05 level of significance.   Explain your conclusion using both the p-value and the test value.

4. State the conclusion?

a)A sample of 30 patients in a doctor's office showed that they had to wait an average of 35 minutes before they could see the doctor. The sample standard deviation is 9 minutes. Assume the population of waiting times is normally distributed.At 90% confidence, compute the margin of error.

b)Consider the population of electric usage per month for houses. The standard deviation of this population is 119 kilowatt-hours. What is the smallest sample size to provide a 90% confidence interval for the population mean with a margin of error of 32 or less? (Enter an integer number.)

1. A sample of 30 Valencia oranges showed a mean weight of 5.5 ounces with a standard deviation of 0.5 ounces. What is the margin of error at 95% confidence?

2. A sample of 30 Valencia oranges showed a mean weight of 5.5 ounces with a standard deviation of 0.5 ounces. What is the 95% confidence interval?

3. A sample of 30 Valencia oranges showed a mean weight of 5.5 ounces with a standard deviation of 0.5 ounces. Do Valencia oranges weigh less than 5.6 ounces? Select the correct formulation:

14. 8. Read the story below from NPR and then identify the very important concept . How does it relate to correlation and Chi-Square

Analysis Finds Geographic Overlap In Opioid Use And Trump Support In 2016

June 23, 20188:02 AM ET

Paul Chisholm, NPR

In 2016, Donald Trump captured 68 percent of the vote in West Virginia, a state hit hard by opioid overdoses.

BRENDAN SMIALOWSKI/AFP/Getty Images

The fact that rural, economically disadvantaged parts of the country broke heavily for the Republican candidate in the 2016 election is well known. But Medicare data indicate that voters in areas that went for Trump weren't just hurting economically — many of them were receiving prescriptions for opioid painkillers.

The findings were published Friday in the medical journal JAMA Network Open. Researchers found a geographic relationship between support for Trump and prescriptions for opioid painkillers.

It's easy to see similarities between the places hardest hit by the opioid epidemic and a map of Trump strongholds. "When we look at the two maps, there was a clear overlap between counties that had high opioid use ... and the vote for Donald Trump," says Dr. James S. Goodwin, chair of geriatrics at the University of Texas Medical Branch in Galveston and the study's lead author. "There were blogs from various people saying there was this overlap. But we had national data."

Goodwin and his team looked at data from Census Bureau, the 2016 election and Medicare Part D, a prescription drug program that serves the elderly and disabled.

To estimate the prevalence of opioid use by county, the researchers used the percentage of enrollees who had received prescriptions for a three-month or longer supply of opioids. Goodwin says that prescription opioid use is strongly correlated with illicit opioid use, which can be hard to quantify.

"There are very inexact ways of measuring illegal opioid use," Goodwin says. "All we can really measure with precision is legal opioid use."

Goodwin's team examined how a variety of factors could have influenced each county's rate of chronic opioid prescriptions. After correcting for demographic variables such as age and race, Goodwin found that support for Trump in the 2016 election closely tracked opioid prescriptions.

In counties with higher-than-average rates of chronic opioid prescriptions, 60 percent of the voters went for Trump. In the counties with lower-than-average rates, only 39 percent voted for Trump.

A lot of this disparity could be chalked up to social factors and economic woes. Rural, economically-depressed counties went strongly for Trump in the 2016 election. These are the same places where opioid use is prevalent. As a result, opioid use and support for Trump might not be directly related, but rather two symptoms of the same problem – a lack of economic opportunity.

To test this theory, Goodwin included other county-level factors in the analysis. These included factors such as unemployment rate, median income, how rural they are, education level, and religious service attendance, among others.

These socioeconomic variables accounted for about two-thirds of the link between voter support for Trump and opioid rates, the paper's authors write. However, socioeconomic factors didn't explain all of the correlation seen in the study.

"It very well may be that if you're in a county that is dissolving because of opioids, you're looking around and you're seeing ruin. That can lead to a sense of despair," Goodwin says. "You want something different. You want radical change."

For voters in communities hit hard by the opioid epidemic, the unconventional Trump candidacy may have been the change people were looking for, Goodwin says.

Dr. Nancy E. Morden, associate professor at the Dartmouth Institute for Health Policy and Clinical Practice, agrees. "People who reach for an opioid might also reach for ... near-term fixes," she says. "I think that Donald Trump's campaign was a promise for near-term relief."

Goodwin's study has limitations and can't establish that opioid use was a definitive factor in how people voted.

"With that kind of study design, you have to be cautious in terms of drawing any causal conclusions," cautions Elene Kennedy-Hendricks, an assistant scientist in the Department of Health Policy and Management at the Johns Hopkins Bloomberg School of Public Health. "The directionality is complicated."

Goodwin acknowledges that the study has shortcomings.

"We were not implying causality, that the Trump vote caused opioids or that opioids caused the Trump vote," he cautions. "We're talking about associations."

Still, the study serves as an interesting example highlighting the links between economic opportunity, social issues and political behavior.

"The types of discussions around what drove the '16 election, and the forces that were behind that, should also be included when people are talking about the opioid epidemic," Goodwin says.

a)A university planner wants to determine the proportion of spring semester students who will attend summer school. Suppose the university would like a 0.90 probability that the sample proportion is within 0.281 or less of the population proportion.What is the smallest sample size to meet the required precision? (There is no estimation for the sample proportion.)  (Enter an integer number.)

b)A university planner wants to determine the proportion of fall semester students who will attend summer school. She surveys 30 current students discovering that 20 will return for summer school.At 90% confidence, compute the margin of error for the estimation of this proportion.

c)For the t distribution with 14 degrees of freedom, calculate P(T < 2.624)!

Suppose X and Y are random variables with joint density f(x, y) = c(x²y + y²), − 1 ≤ x ≤ 1, 0 ≤ y ≤ 1 (0 else).

a) Find c.

b) Determine whether X and Y are independent.

c) Compute P(3X + 2Y > 1 | −1/2 ≤ X ≤ 1/2).

Consider the set of five numbers {0, 2, 4, 6, 8}.

1) Make a list of all possible samples of size 2 that can be drawn from this set of integers. (Sample without replacements, that is, once a number is selected, you don’t put it back in the sample set.)

2) Make a list of all possible sample means for samples of size 2 selected from this set.

3) List the distribution of the sample means and construct a histogram of this distribution.

Jaqueline and Pedro are running a marathon. Jaqueline's time for finishing a marathon is uniformly distributed between 150 minutes and 180 minutes. Pedro's time for finishing a marathon is uniformly distributed between 160 and 190 minutes. Calculate the probability that Jaqueline beats Pedro to the finish line. Give answer as a decimal rounded to 4 places.

If a symmetric coin is tossed 100 times, by using normal approximation find the probability that:

a. it comes up H more than 60 times

b. the number of H(X) is between 60 and 90 (60≤X≤90)

An important application of regression analysis in accounting is in the estimation of cost. By collecting data on volume and cost and using the least squares method to develop an estimated regression equation relating volume and cost, an accountant can estimate the cost associated with a particular manufacturing volume. Consider the following sample of 7 production volumes and total cost data for a manufacturing operation.

1. Use these data to estimate a regression equation that could be used to predict the total cost for a given production volume. Intercept ______ and Slope ______
2. What is the marginal cost per unit produced? (Remember what marginal cost is from Principle of Economics?)
3. The company’s production schedule shows 500 units must be produced next month. What is the estimated total cost for this operation?

A psychologist wants to determine whether speaking more than one language fluently has cognitive benefits. They conduct a study in which a total of 72 participants are tested on a task measuring cognitive control. Half the participants are male, and half are female and speak one, two, or three+ languages fluently. For a two-way ANOVA with SS_between = 148; SS_Language = 80; SS_Sex = 50; SS_total = 350, what can the psychologist conclude? Be sure to address all hypotheses. Assume the DV is continuous.

Investigators need to study the impact of the Coronavirus outbreak. It is of interest to understand how the number of hospitalizations in a particular state is associated with three predictors including the number of tests available, whether the social distancing measures are taken, and the overall population size. Answer the questions below: 1. Identify the outcome variable and its type (continuous, or binary, or count). 2. What are the predictor variables? 3. (Give the name of the model that you would like to use for this problem, and explain the reason for using the model. Do not need to write down the mathematical expression of the model.

AM -vs- PM Test Scores: In my PM section of statistics there are 30 students. The scores of Test 1 are given in the table below. The results are ordered lowest to highest to aid in answering the following questions.

(a) The value of P₉₀ is  .

(b) Complete the 5-number summary.

A recent article in a local magazine indicated that the mean selling price of homes in the area is less than $232,000. Can we conclude that the mean selling price in the area is less than $232,000? Use the 0.01 significance level. {Use 232.0 as the value, not 232,000.}

Assume the list is a sample.

Requirement following the hypotheses testing 6-step process:

• State Null and Alternative Hypotheses,
• State the significance level.
• State which distribution is used.
• State the decision rule including graph.
• State the test statistic and the p-value.
• State the conclusion.

Notes:

• Use 232.0 instead of 232,000.
• State z-values to 2 decimal places unless 3 decimal places are needed; State t-values to 3 decimal places; State p-values to 4 decimal places.

(1 point) In a study of red/green color blindness, 550 men and 2300 women are randomly selected and tested. Among the men, 47 have red/green color blindness. Among the women, 7 have red/green color blindness. Test the claim that men have a higher rate of red/green color blindness.
(Note: Type ‘‘p_m′′‘‘p_m″ for the symbol pmpm , for example p_mnot=p_wp_mnot=p_w for the proportions are not equal, p_m>p_wp_m>p_w for the proportion of men with color blindness is larger, p_m<p_wp_m<p_w , for the proportion of men is smaller. )

(a) State the null hypothesis:

(b) State the alternative hypothesis:

(c) The test statistic is

(e) Construct the 9595% confidence interval for the difference between the color blindness rates of men and women.