**Hypothesis Testing of Mean Human Temperature**It has long been stated that the mean temperature of humans is 98.6°F. However, two researchers currently involved in the subject thought that the mean temperature of humans is less than 98.6°F. They measured the temperatures of 50 healthy adults 1 to 4 times daily for 3 days, obtaining 225 measurements. The sample data resulted in a sample mean of 98.3°F and a sample standard deviation of 1°F. Use the P-value approach to conduct a hypothesis test to judge whether the mean temperature of humans is less than 98.6°F at the α = 0.01 level of significance.**State the Hypotheses**- \( H_0: \) (1) _______ (2) _______ 98.6°F- \( H_1: \) (3) _______ (4) _______ 98.6°F**Find the Test Statistic**- \( t_0 = \) _______ (Round to two decimal places as needed.)**The P-value is** _______ (Round to three decimal places as needed.)**What can be concluded?**- **A.** Reject \( H_0 \) since the P-value is not less than the significance level.- **B.** Reject \( H_0 \) since the P-value is less than the significance level.- **C.** Do not reject \( H_0 \) since the P-value is less than the significance level.- **D.** Do not reject \( H_0 \) since the P-value is not less than the significance level.

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Answered: It has long been stated that the mean…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 435 gram setting. It is believed that the machine is underfilling the bags. A 35 bag sample had a mean of 427 grams. Assume the population standard deviation is known to be 17. A level of significance of 0.05 will be used. State the null and alternative hypotheses.
An automobile manufacturer claims that its van has a 36.7 miles/gallon (MPG) rating. An independent testing firm has been contracted to test the MPG for this van since it is believed that the van has an incorrect manufacturer's MPG rating. After testing 140 vans, they found a mean MPG of 37.0. Assume the standard deviation is known to be 1.4. A level of significance of 0.05 will be used. Find the value of the test statistic. Round your answer to 2 decimal places. Enter the value of the test statistic. Answer How to enter your answer (opens in new window) Keypad Keyboard Shortcuts Tables
Many cheeses are produced in the shape of a wheel. Because of the differences in consistency between these different types of cheese, the amount of cheese, measured by weight, varies from wheel to wheel. Heidi Cembert wishes to determine whether there is a significant difference, at the 10% level, between the weight per wheel of Gouda and Brie cheese. She randomly samples 18 wheels of Gouda and finds the mean is 1.3 lb with a standard deviation of 0.3 lb; she then randomly samples 10 wheels of Brie and finds a mean of 0.95 lb and a standard deviation of 0.21 lb. What is the df and p-value for Heidi's hypothesis of equality? Assume normality. (Give your answer correct to four decimal places.)
The mean consumption of water per household in a city was 1244 cubic feet per month. Due to a water shortage because of a drought, the city council campaigned for water use conservation by households. A few months after the campaign was started, the mean consumption of water for a sample of 96 households was found to be 1164 cubic feet per month. The population standard deviation is given to be 257 cubic feet. a. Find the p-value for the hypothesis test that the mean consumption of water per household has decreased due to the campaign by the city council. Would you reject the null hypothesis at a = 0.025? Round your answer to four decimal places. p-value = We i b. Make the test of part a using the critical-value approach and a = 0.025. Zobserved Round your answer for z to two decimal places. We Ho. i Ho. We conclude that the mean consumption of water per household has due to the campaign by the city council.
A factory that manufactures screws is performing a quality control experiment. Each object should have a length of no more than 13 centimeters. The factory believes that the length of the screws exceeds this value and measures the length of 70 screws. The sample mean screw length was 13.01 centimeters. The population standard deviation is known to be σ=0.15 centimeters. What is the null hypothesis? What is the alternative hypothesis?
In a randoms sample of six people, the mean driving distance to work was 19.7 miles and the standard deviation was 6.1 miles. Assume the population is normally distributed and use the t-distribution to find the margin of error and construct a 90% confidence interval for the population mean u. Interpret the results.
Sony would like to test the hypothesis that the average age of a PlayStation user is different from the average age of an Xbox user. A random sample of 32 PlayStation users had an average age of 33.7 years while a random sample of 36 Xbox users had an average age of 35.6 years. Assume that the population standard deviation for the age of PlayStation and Xbox users is 3.7 and 3.5 years, respectively. Also assume population variances are equal. Sony would like to set alpha= 0.05. The 95% confidence interval for the difference in population means is
The Chancellor wants you to calculate the sample size needed with a margin of error of 15, 99% confidence, and a population standard deviation of 22.
A tire company claims that the lifetimes of its tires average 50,000 miles. The standard deviation of tire lifetimes is known to be 5,261 miles. You sample 100 tires and will test the hypothesis that the mean tire lifetime is at least 50,000 miles against the alternative that it is less. Assume, in fact, that the true mean lifetime is 49,545 miles. It is decided to reject Ho if the sample mean is less than 48,894. Find the level and power of this test. 0 Round your answers to four decimal places. Level of the test = Power of the test =
In 16 women with diabetes, the morning blood sugar mean was 49.4 with a standard deviation of 24.0. In normal healthy women, the mean was 47.0. From the sample information, can we conclude that the blood sugar mean in women with rheumatoid arthritis is greater than that in normal women? Assume a significance level of 0.05.
According to an article in Good Housekeeping, a 128-lb woman who walks for 30 minutes four times a week at a steady, four-mi/hr pace can lose up to 10 lbs over a span of a year. Suppose 35 women with weights between 125 and 130lb perform the four walks per week for a year and at the end of the year the average weight loss for the 35 was 9.1 lbs. If the sample standard deviation is 5, calculate the value of the test statistic and find the p-value of the hypothesis test of Ho:µ =10 vs H1:µ≠10.
The standard deviation of a sample is 3.0 and the standard error is -16.52, what was the original sample size?

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