In a test of the hypothesis H0: μ=10 versus Ha: μ≠10​, a sample of n=50 observations possessed mean x=10.8 and standard deviation s=3.1. Find and interpret the​ p-value for this test.   The​ p-value for this test is _______.​ (Round to four decimal places as​ needed.)

A random sample of 100 observations from a population with standard deviation 39 yielded a sample mean of 107. Complete parts a throughc below. a. Test the null hypothesis that u = 100 against the alternative hypothesis that u > 100, using a =0.05. Interpret the results of the test. What is the value of the test statistic? (Round to two decimal places as needed.) z=

Use the following information for Questions 19-21. Teresa works at a medium-sized doctor's office and notices that appointment times are approximately normally distributed with mean 25 minutes and standard deviation 10 minutes. A patient complains that the wait times are too long and that her average wait time is much longer than 25 minutes. Teresa decides to conduct a test with a = 0.05 and the following hypotheses Ho: H=25 vs. Ha:μ> 25 Teresa randomly selects 25 appointments and records their times and finds their mean. The P-value of the test of the null hypothesis is O the probability the null hypothesis is false. O the probability, assuming the null hypothesis is true, that the test statistic will take a value at least as extreme as that actually observed. O the probability, assuming the null hypothesis is false, that the test statistic will take a value at least as extreme as that actually observed. O the probability the null hypothesis is true.

Suppos are interested in studying a population to estimate its mean. The population is normal and has a standard deviation of G=23. We have taken a random sample of size 11=95 from the population. This is Sample 1 in the table below. (In the table, Sample 1 is written "S1", Sample 2 is written "S2", etc.) As shown in the table, the sample mean of Sample 1 is = 142.0. Also shown are the lower and upper limits of the 80% confidence interval for the population mean using this sample, as well as the lower and upper limits of the 95% confidence interval. Suppose that the true mean of the population is = 140, which is shown on the displays for the confidence intervals. Press the "Generate Samples" button to simulate taking 19 more random samples of size 11 = 95 from this same population. (The 80% and 95% confidence intervals for all of the samples are shown in the table and graphed.) Then complete parts (a) through (c) below the table. 80% 80% 95% 95% lower upper lower upper limit limit…

If the t-statistic for a single sample t-test is 1.58, what can you conclude? a. The test is significant at an alpha level of .05. b. The sample size of the test was at least 30. c. The sample mean was larger than the population mean. d. The population standard deviation was smaller than the difference between the sample mean and the population mean.

An online survey company claims their surveys take on average less than 20 minutes to complete. Before running a new ad campaign, they need data to prove that the average completion time is actually less than 20 minutes. The company randomly samples 15 surveys taken in the last week and found a sample mean of 17 minutes with a sample standard deviation of 5 minutes.   What is the alternative hypothesis of this test. Be sure to include symbol and number needed to form the hypothesis. HA : µ  Find the test statistic for this test.   (round answer to 3 decimal places)  Find the p-value for this test.   (round answer to 3 decimal places)

A population has a mean of  1398.25 and standard deviation of 246.85   16 If we kept n at 82 but reduced the error probability to α = 0.01, the magin of error would ... a Decrease by 20% b Increase by 20% c Increase by 31% d Increase by 24%

In conducting a test on the hypotheses Ho: μ = 50 and Ha: μ > 50, you find that the population mean is 55 when it is actually 50. This results in what type of error? O No error ○ Type I error ○ Type II error Standard deviation of the mean O There is not enough information given

The daily wage of a particular industry is normally distributed with a mean of 150 pesos. In a random sample of 144 workers of a very large company in this industry, the mean daily wage was found to be 148 pesos with a standard deviation of 10 pesos. Can this company be accused of paying inferior wages (less than the usual) at α=5%? Which of the following sets of hypotheses should be used in this study? A. Ho: μ = 150 vs. Ha: μ > 150 B. Ho: μ = 150 vs. Ha: μ < 150 C. Ho: μ = 148 vs. Ha: μ > 148 D. Ho: μ = 148 vs. Ha: μ < 148

33.6 and o = 37.1. If a random sample of size A normal distributed population has parameters u n = 51 is selected, a. What is the mean of the distribution of sample means? b. What is the standard deviation of the distribution of sample means? Round to two decimal places.