A Realtor claims that no more than half of the homes he sells are sold for less than the asking price. When reviewing a random sample of 12 sales over the past year, he found that actually 7 were sold below the asking price. (b-1) Calculate a p-value for the observed sample outcome, using the normal distribution. (Round your z-value to 2 decimal places. Round your answer to 4 decimal places.)   (c) Use Excel to calculate the binomial probability P(X ≥ 7 | n = 12, ππ = .50) = 1 − P(X ≤ 6 | n = 12, ππ = .50). (Round your answer to 4 decimal places.)

The price to earnings ratio (P/E) Is an Important tool in financial work. A random sample of 14 large U.S. banks (JP Morgan Chase, Bank of America, and others) gave the following P/E ratios.t 24 16 22 14 12 13 17 22 15 19 23 13 11 18 The sample mean is x = 17.1. Generally speaking, a low P/E ratio indicates a "value" or bargain stock. Suppose a recent copy of a magazine indicated that the P/E ratio of a certain stock index is H = 18. Let x be a random variable representing the P/E ratio of all large U.S. bank stocks. We assume that x has a normal distribution and o = 4.7. Do these data indicate that the P/E ratio of all U.S. bank stocks is less than 18? Use a = 0.01. (a) What is the level of significance? State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test? O Ho: H = 18; H1: H # 18; two-tailed O Ho: H = 18; H1: H 18; right-tailed %3D O Ho: H # 18; H1: H = 18; two-tailed (b) What sampling distribution will you use? Explain the rationale…

A researcher would like to evaluate the effectiveness of a pain-relief patch designed for lower back pain. Prior to testing the patch, each of n = 8 patients rates the current level of back pain on a scale from 1 to 10. After wearing the patch for 90 minutes, a second pain rating is recorded. The data are as follows: Include in your responses: A. Compute the mean and variance for the sample of difference scores. B. Provide the Null and alternative hypotheses  C. Calculate SSD

A pharmaceutical company makes tranquilizers. It is assumed that the distribution for the length of time they last is approximately normal. Researchers in a hospital used the drug on a random sample of 9 patients. The effective period of the tranquilizer for each patient (in hours) was as follows: 2.5; 2.8; 3.1; 2.3; 2.3; 2.2; 2.8; 2.1; and 2.4.   1.Which distribution should you use for this problem? (Enter your answer in the form z or tdf where df is the degrees of freedom.)    2. Construct a 95% confidence interval for the population mean length of time.  (i) State the confidence interval. (Round your answers to two decimal places.) (     ,     )   (iii) Calculate the error bound. (Round your answer to two decimal places.)

A pharmaceutical company makes tranquilizers. It is assumed that the distribution for the length of time they last is approximately normal. Researchers in a hospital used the drug on a random sample of 9 patients. The effective period of the tranquilizer for each patient (in hours) was as follows: 2.5; 2.9; 3.1; 2.3; 2.3; 2.2; 2.8; 2.1; and 2.4.

(a ) Calculate the mean of the distribution . (b ) Calculate the 10% trimmed mean . ( c) Why is the trimmed mean a better summary of the center of this distribution than the mean?

Imagine that a researcher wants to compare the intelligence levels of Poodles to all dogs.  He hypothesizes that Poodles will score differently than other dogs.  He uses a standard test of dog intelligence in his study. The population of all dogs has a mean of μ = 100, and an SD of 15.  He obtains a random sample of 500 Poodles and he finds that the mean intelligence score of the sample is 117.   Is this a one- or two- tailed test? Write the Ho and Ha for this research question. What kind of statistic should be calculated to test the hypothesis? Compute that statistic by hand What should the researcher conclude? Write a blurb describing the results

A researcher would like to evaluate the effectiveness of a pain-relief patch designed for back pain. Prior to testing the patch, each of n = 8 patients rates their current level of back pain on a scale from 1 to 10. After wearing the patch for 90 minutes, a second pain rating is recorded. The data are as follows:                  Before  After                      6         2                      8         3                      9         4                      8         1                    10         2                      5         3                      9         8                      7         7   a. Compute the mean and variance for the sample of difference scores. ​ b. Do the results indicate that the pain-relief patch has an effect? Use a two-tailed test with α = .05 ​ c. Compute Cohen’s d to measure the size of the effect.

In a fishing lodge brochure, the lodge advertises that 75% of its guests catch northern pike over 20 pounds. Suppose that last summer 59 out of a random sample of 85 guests did, in fact, catch northern pike weighing over 20 pounds. Does this indicate that the population proportion of guests who catch pike over 20 pounds is different from 75% (either higher or lower)? Use a = 0.05. (a) What is the level of significance? State the null and alternate hypotheses. O Ho: p = 0.75; H1: p 0.75 (b) What sampling distribution will you use? O The Student's t, since np 5 and ng > 5. O The standard normal, since np 5 and nq > 5. What is the value of the sample test statistic? (Round your answer to two decimal places.) (c) Find the P-value of the test statistic. (Round your answer to four decimal places.)

A researcher wants to investigate the effects of environmental factors on IQ scores. For an initial study, she takes a sample of 400 people who grew up as the only child. She finds that 48.5% of them have an IQ score over 100. It is known that 50% of the general population has an IQ score exceeding 100. (a) Find the mean of p, where p is the proportion of people with IQ scores over 100 in a random sample of 400 people. (b) Find the standard deviation of p. (c) Compute an approximation for P(p is greater than or equal to 0.485), which is the probability that there will be 48.5% or more individuals with IQ scores over 100 in a random sample of 400. Round answer to 4 decimal places.