2 Section 7.4 INFERENCE FOR MEANS
1) Example: The World Health Organization (WHO) monitors many variables to
assess a population's overall health. One of these variables is birth weight. A low
birth weight is defined as 2500 grams or less.
Suppose that babies in a town had a mean birth weight of 3,500 grams with a
standard deviation of 500 grams in 2005. This year, a random sample of 25
babies has a mean weight of 3,400 grams. Obviously, this sample weighs less on
average than the population of babies in the town in 2005. A decrease in the
town's mean birth weight could indicate a decline in overall health of the town.
Are differences this large expected in random sampling from a population with a
mean birth weight of 3,500 grams? What is the probability that a random sample
of 25 babies will have a mean birth weight of 3,400 grams or less?
We assume that the variability in individual birth weights is the same this year
as it was in 2005. In general, body measurements in a large population can be
modeled by a normal curve.
Section 7.4 DISTRIBUTION OF SAMPLE MEANS
Here are the two normal models drawn
on the same scale. Which is the
population and which is the sampling
distribution? How do you know?
d) What is the z-score for a baby that weighs 3400 grams? What is the z-score
for a sample of babies with a mean birth weight of 3400 grams? Why do your
answers make sense when you look at the normal curves in (c)?
e) What is the probability that a random sample of 25 babies weighs 3,400
grams or less? (Shade the area representing the probability in the
appropriate normal curve in (c) and give your estimate.)
f) Is the difference between 3,400g and 3,500g statistically significant? Or is
this difference what we expect to see in random sampling when the
population has a mean of 3,500g? How do you know?
3

WOULD YOU BE ABLE TO HELP ME WITH f) Is the difference between 3,400g and 3,500g statistically significant? Or is
this difference what we expect to see in random sampling when the
population has a mean of 3,500g? How do you know?

---Find the 98% confidence interval for the difference between two means based on this information about two samples. Assume independent samples from normal populations. (Use conservative degrees of freedom.) (Give your answers correct to two decimal places.)

---Find the value of t for the difference between two means based on an assumption of normality and this information about two samples. (Use sample 1 - sample 2. Give your answer correct to two decimal places.)

---If a random sample of 20 homes south of a town has a mean selling price of $145,375 and a standard deviation of $4825, and a random sample of 23 homes north of a town has a mean selling price of $148,550 and a standard deviation of $5925, can you conclude that there is a significant difference between the selling price of homes in these two areas of the town at the 0.05 level? Assume normality.

(a) Find t. (Round your answer to two decimal places.)


(ii) Find the p-value. (Round your answer to four decimal places.)

---Twenty laboratory mice were randomly divided into two groups of 10. Each group was fed according to a prescribed diet. At the end of 3 weeks, the weight gained by each animal was recorded. Do the data in the following table justify the conclusion that the mean weight gained on diet B was greater than the mean weight gained on diet A, at the α = 0.05 level of significance? Assume normality. (Use Diet B - Diet A.)

(a) Find t. (Give your answer correct to two decimal places.)


(ii) Find the p-value. (Give your answer correct to four decimal places.)

Wall Street Journal article: San Francisco apartments market - Read the article and answer the questions at the end

Once Booming San Francisco Apartment Market Goes in Reverse City’s vacancy rate rose to 6.2% in May, up from 3.9% only three months ago

By Will Parker June 18, 2020 5:30 am ET

Rents in San Francisco, the most expensive apartment market in the U.S., are tumbling as the city’s vaunted tech sector sheds jobs and more tenants leave the city.

The apartment vacancy rate in San Francisco rose to 6.2% in May, according to apartment data firm RealPage. That’s up from 3.9% only three months ago, after stay-at-home orders went into effect and more people in the city decided not to renew their leases.

San Francisco’s median rent in May for a one-bedroom apartment was also down 9.2% compared with a year ago at $3,360 a month, according to listings platform Zumper. That was still the highest monthly rent of all major U.S. markets, Zumper said, and a reminder of how steeply rents in the city climbed before their more recent descent.

The dot-com boom of the 1990s drove San Francisco real-estate prices and fueled rent increases, while zoning limitations and high construction costs have kept new apartment supply in check. In more recent years, a growing number of tech employees have flocked to San Francisco, with more opting to take buses to nearby Silicon Valley corporate campuses from the city rather

than living in the suburbs.

Tall Buildings, Lower Rents Apartment asking rents are dropping in majormetros across the country Percentage change in median one-bedroomrents from May 2019 to May 2020 Source: Zumper Boston Los Angeles Chicago Denver 0-7.5% -5 -2.5 Now, the pandemic is upending San Francisco’s workforce more than in most cities, remaking part of its corporate landscape. Several large, high-paying companies, including Yelp Inc., and Lyft Inc., have begun laying off workers in the city. LendingClub reported to the California Employment Development Department earlier this month that it was permanently laying off 306 San Francisco employees.

San Francisco-based startup Stitch Fix Inc., meanwhile, is looking to save costs by hiring or relocating staff to cheaper cities outside of California like Pittsburgh and Cleveland. PG&E Corp. said this month it plans to move to Oakland, ending more than 100 years in San Francisco.

Other Bay Area businesses are allowing their employees to work from home indefinitely, making some San Franciscans question whether it still makes sense to pay exorbitant rents when they no longer have to live in the same city as their office.

“This is a very unusual market,” said local real-estate agent Joanne Fazzino. “Landlords can’t expect the same kind of rents they were expecting.”

San Francisco isn’t the only high-rent city brought back to earth. In Manhattan, the rental apartment vacancy rate is now at its highest point in at least 14 years, according to a report by real estate appraiser Jonathan Miller and brokerage Douglas Elliman. And RealPage found that for all of New York City, renters are signing leases at more than 8% off asking price on

average. Meanwhile, home sales are booming in the city’s suburbs.

Other cities that experienced high rent growth, like Nashville, Tenn.; Orlando, Fla.; Atlanta and Charlotte, N.C., have seen rental vacancy rates grow to 5% or more, according to data from RealPage.

In places where rents aren’t falling, price growth is easing. The pace of rent growth has slowed in 27 major markets over the past year, including Seattle and Austin, Texas, with rents actually falling in 11 of those 27 markets in just the past month, according to real-estate firm Zillow.

But Northern California is among the hardest hit. Rents for one-bedroom apartments are falling in San Francisco, San Jose and Fresno, and are close to flat in Oakland and Sacramento, according to Zumper. Rent cuts on new leases are 8% or more on average in both San Francisco and San Jose, RealPage said.

Still, a few hundred dollars shaved off the rent doesn’t bring prices down to what most people would think of as affordable. The Bay Area has a higher rate of rent-burdened households than do most parts of the country, defined as households spending more than 30% of their gross income on rent.

San Francisco’s City Hall is helping out. Last week, it decided to make permanent a temporary eviction moratorium, which was put in place to protect tenants from being evicted for failure to pay rent during the pandemic. The many renters protected from eviction could actually be preventing the city’s vacancy rate from being even higher.

Some market analysts think tenants shouldn’t expect rents to fall much further. Prices of homes for sale are also not coming down, and that ultimately pushes more people in renting, propping up demand for apartments.

For now, however, it is a renter’s market for a change. Sandeep Giri and his wife, Sunita, began searching for a new San Francisco home in April. For the first several weeks, they offered less than the asking rent. Rental managers wouldn’t even respond. But in June, the couple found a

three-bedroom, single-family home with an asking price of $5,800. The Giris’ lower offer of $5,400 was accepted without question.

“We were really pleasantly surprised,” he said.

The hunt played out very differently when Mr. Giri rented his first apartment during the late 1990s dot-com boom. “We had to literally stand in a long line of applicants, with a résumé and our credit score all printed out in our hands and people would like, outbid you, right in front of you,” he said.

Questions:

1. The article mentioned that the vacancy rate for apartments in San Francisco rose from 3.9 percent in February to 6.2 percent in May. Briefly explain how the rental market changed as the vacancy rate rose. How was the equilibrium price and quantity of apartments affected by this change?

2. The market for apartments in San Francisco is subject to rent control, which limits the amount of rent tenants can be charged and how much the cost of capital improvements can be passed on by landlords to their tenants. What impact does the imposition of rent control have on the quantity demanded of apartments? What impact does rent control have on the quantity supplied of apartments?

3. From the article: “For now…it is a renter’s market for a change.” Briefly explain what is meant by a “renter’s market.”

4. In the article, Sandeep Giri described the first time he and his wife searched for an apartment in San Francisco during the late 1990s: “We had to literally stand in a long line of applicants, with a résumé and our credit score all printed out in our hands and people would …outbid you….” What does this statement imply about the relationship between the quantity supplied and the quantity demanded of apartments in San Francisco in the late 1990s? Briefly explain your answer.

1. Mention three main ideas of the classical school, which were accepted by Karl Marx .

What are the benefits of announcing school events on social media channels from different stakeholders' perspectives?

Summarize the different approach in school safety such as metal detectors arm guard and 0 tolerance Policies

Taryn is a high school senior who is undergoing a strenuous running regimen for several hours a day in order to qualify for her state high school track meet. Lately she has experienced intense pain in her right leg that is hindering her workouts. Her physician performs an examination of her right leg. The doctor doesn’t notice any outward evidence of injury; he then orders a bone scan. What does her doctor suspect the problem is?