posted by .

1(a)Let Y have a binomial distribution with parameters n and p. We reject Ho: p=1/2 and accept H1: p>1/2 if Y>=c. Find n and c such that the probability of a Type I error is .10, and P(reject Ho/p=2/3)=.95.
(b)What is the probability of a Type II error?

2.Let xbar be the observed mean of a random sample of size n from a distribution having mean mu and variance sigma squared. Find n so that xbar-sigma/4 to xbar+sigma/4 is an approximate 95% confidence interval for mu.

3. Let p denote the probability that, for a particular tennis player, the first serve is good. Since p=0.40 this player decided to take lessons in order to increase p. When the lessons are completed, the hypothesis Ho:p=0.40 will be tested against H1:p>0.40 based on n=25 trials. Let y equal the number of first serves that are good, and let the critical region be defined by C={y:y>=13}. Determine the significance level.

4. Let X be N(mu,sigma squared)so that P(X<89)=0.90 and P(X<94)=0.95. Find mu and sigma squared.

5. Let X1,...,X9 be a random sample of size 9 from a distribution that is N(mu,sigma squared). If sigma is known, find the length of a 95% confidence interval for mu if this interval is based on the random variable Squarert9(xbar-mu)/sigma.

6. Half pint (8oz) milk cartons are filled at a dairy by a filling machine. To provide a check on the machine, a sample of 10 cartons is periodically measured. If the sample mean deviates by more than a certain amount d from the nominal value 8oz, i.e, if [xbar-8]>d, then the machine setting is adjusted. The chance of a false alarm indicating an unnecessary adjustment is to be limited to 1%. Find a formula for d.

7. The lifetime of lightbulbs of a particular type are normally distributed with a mean of 293 hours and a standard deviation of 6 hours. Find the 1st quartile.

## Similar Questions

1. ### statistics

In a chi-squared test of a contingency table, the value of the test statistic was =12.678, and the critical value at = 0.025 was 14.4494. Thus, (Points: 2) A) we fail to reject the null hypothesis at = 0.025 B) we reject the null hypothesis …
2. ### college

The diameter of a wire should be 8 cm. It follows a normal distribution and has a standard deviation of 0.01 cm. A person tests each delivery by taking 5 samples, accepting the goods only if the mean is at most 8.01 a) Find the probability …
3. ### Statistics

Test the significance of the correlation coefficient r at a=0.05 for the data below. X values 59, 65, 73, 80, 89 Y values 97, 102, 110, 117, 125 A) Accept p=0 because 60.81<3.18 B) Reject p=0 because 61.13>3.18 C) Accept p=0 …
4. ### Statistics

You have an SRS of size n = 16 from a Normal distribution with standard deviation = 1. You wish to test H_0 :Î¼ = 0 H_a :Î¼ > 0 You decide to reject H_0 if x bar > 0 and to accept H_0 otherwise. a. Find the probability of …
5. ### statistics

2. We would like to test whether the population mean is less than 40. Suppose that a hypothesis test is conducted to determine if the mean of the population has decreased or not. Describe what a Type II error would mean for this example. …
6. ### Probability and Statistics

The proportion of adults living in a small town who are college graduates is estimated to be p = 0.6. To test this hypothesis, a random sample of 15 adults is selected. If the number of college graduates in the sample is anywhere from …
7. ### Probability and Statistics

The proportion of adults living in a small town who are college graduates is estimated to be p = 0.6. To test this hypothesis, a random sample of 15 adults is selected. If the number of college graduates in the sample is anywhere from …
8. ### Probability and Statistics

The proportion of adults living in a small town who are college graduates is estimated to be p = 0.6. To test this hypothesis, a random sample of 15 adults is selected. If the number of college graduates in the sample is anywhere from …
9. ### Probability and Statistics

The proportion of adults living in a small town who are college graduates is estimated to be p = 0.6. To test this hypothesis, a random sample of 15 adults is selected. If the number of college graduates in the sample is anywhere from …
10. ### ap statistics

In hypothesis testing, β is the probability of committing an error of Type II. The power of the test, 1 - β, is then: A. the probability of failing to reject H0. B. the probability of rejecting H0 when HA is true C. the probability …

More Similar Questions