Get Expert Answers to Your Bivariate Data Questions

If r is closer to zero x and y are unrelated 

An MP3 manufacturer claimsthat 65% of teenagers 13 to 16 years old have their own MP3 players.
A researcher wishes to test the claim and selects a random sample of 80 teenagers. She finds that
57 have their own MP3 players. At � = 0.05, should the claim be rejected?

The average credit card debt for a recent year was $9205. Five years earlier the average credit card
debt was $6618. Assume sample sizes of 35 were used and the population standard deviations of
both samples were $1928. Find the 95% confidence interval of the difference in means.

J. P. Morgan Asset Management publishes information about financial investments. Between 2002 and 2011 the expected return for the S&P was with a standard deviation of and the expected return over that same period for a Core Bonds fund was with a standard deviation of (J. P. Morgan Asset Management, Guide to the Markets). The publication also reported that the correlation between the S&P and Core Bonds is . You are considering portfolio investments that are composed of an S&P index fund and a Core Bonds fund. a.  Using the information provided, determine the covariance between the S&P and Core Bonds. Round your answer to two decimal places. If required enter negative values as negative numbers.

the probability that a mash stick will break on been stroked is 0.4.what is the probability that out of 50 sticks striken 

a) non will break

b)more than one stick will break

Driven by technological advances and financial pressures, the number of surgeries performed in physicians' offices nationwide has been increasing over the years. The function ${\displaystyle f\left(t\right)=-0.00447t^3+0.09864t^2+0.05192t+0.8(0\le t\le 15)}$ gives the number of surgeries (in millions) performed in physicians' offices in year t, with $t=0$ corresponding to the beginning of 1986.
a. Plot the graph of f in the viewing window $[0,15]\times [0,10]$.
b. Prove that f is increasing on the interval [0, 15].

Consider a random sample of size n = 31, with sample mean ${\displaystyle \bar{x}=45.2}$ and sample standard deviation s = 5.3. Compute 90%, 95%, and 99% confidence intervals for \muμ using Method 1 with a Student's t distribution. Round endpoints to two digits after the decimal.

The following advanced exercise use a generalized ratio test to determine convergence of some series that arise in particular applications, including the ratio and root test, are not powerful enough to determine their convergence. The test states that if $$ ${\displaystyle lim\{n\to \mathrm{\infty }\}\frac{a\left\{2n\right\}}{a_n}<\frac{1}{2}}$ then $\sum a_n$converges,while if ${\displaystyle lim\{n\to \mathrm{\infty }\}\frac{a\{2n+1\}}{a_n}>\frac{1}{2}}$, then $\sum a_n$ diverges.

Let ${\displaystyle a_n=\frac{1}{1+x}\frac{2}{2+x}\dots \frac{n}{n+x}\frac{1}{n}=\frac{(n-1)!}{(1+x)(2+x)\dots (n+x)}}$.

Show that $\frac{a_{2n}}{a_n}\le \frac{e^{-x/2}}{2}$ . For which x > 0 does the generalized ratio test imply convergence of $\sum _{n=1}^{\mathrm{\infty }}{a}_n$?

B. G. Cosmos, a scientist, believes that the probability is ${\displaystyle \frac{2}{5}}$ that aliens from an advanced civilization on Planet X are trying to communicate with us by sending high-frequency signals to Earth. By using sophisticated equipment, Cosmos hopes to pick up these signals. The manufacturer of the equipment, Trekee, Inc., claims that if aliens are indeed sending signals, the probability that the equipment will detect them is ${\displaystyle \frac{3}{5}}$. However, if aliens are not sending signals, the probability that the equipment will seem to detect such signals is $\frac{1}{10}$. If the equipment detects signals, what is the probability that aliens are actually sending them?