If a sample of 50 individuals was taken from a population with a standard deviation of 12 and the sample mean is 95, what is the t-statistic for a two-tailed hypothesis test at a significance level of 0.05?
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A sample of 50 individuals was taken from the population.
Sample size,
Sample mean,
Population standard deviation,
level of significance,
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- In a study of computer use, 1000 randomly selected Canadian Internet users were asked how much time they spend using the Internet in a typical week. The mean of the sample observations was 12.6 hours. (a) The sample standard deviation was not reported, but suppose that it was 4 hours. Carry out a hypothesis test with a significance level of 0.05 to decide if there is convincing evidence that the mean time spent using the Internet by Canadians is greater than 12.4 hours. (Use a statistical computer package to calculate the P-value. Round your test statistic to two decimal places and your P-value to three decimal places.) t = P-value =Two species of fish have similar phenotypes to each other, researchers wonder if they can classify these fish species based on their sizes. One species has mean size of 10cm, with standard deviation of 1. The other species has mean size of 12cm, with standard deviation of 2. Size of 15 fish from each species were measured. a. Which hypothesis testing method can be used to compare the mean size of the two populations? Perform the test for a = 0.01. How does result of this test help the researchers to decide if they can classify these fish species based on their sizes? b. What is the power of the test? How does power of the test help the researchers to decide if they can classify these fish species based on their sizes?A researcher wants to compare the effectiveness of two different study techniques for a test. The mean test score for the first technique is 75 with a standard deviation of 5, and the mean test score for the second technique is 80 with a standard deviation of 4. The sample size for each group is 20. What is the 95% Confidence Interval for the difference in the mean test scores for the two techniques?
- In a hypothesis test, if the null hypothesis states that the population mean is equal to 100 with a standard deviation of 15, and the sample mean is 108 with a sample size of 36, what is the calculated z-score for this test?NebNas manages the credit department for a grocery store chain in the province, and she would like to determine whether the mean monthly balance of credit card holders is equal to $95. A random sample of 100 accounts indicated that the mean owed is $101.5 with a sample standard deviation of $25.6. If she wanted to test whether the mean balance is different from $95 and decided to reject the null hypothesis, what will be the p-value of the test?A quiz related to digital knowledge was conducted. The quiz had 10 questions and covered topics such as the purpose of browser cookies, phishing scams, and privacy policies. The survey was given to 50 people. The mean score is 4.1 with a standard deviation of 2.6. We want to know if the data provide evidence that the mean score in the population is lower than 5. We will use alpha = 0.05 to make our decision. What is the null hypothesis for this question? Group of answer choices a. The proportion of people who pass the test is 5. b. The mean test score of the population is 5. c. The mean test score of the 50 people who took the test is 5. d.The standard deviation is 2.6
- You were told that the mean daily cost of a hotel room in downtown St. Louis is $120. You will be needing to rent a hotel room there in the near future and you want to find the best rate. You randomly select a sample of 18 hotel rooms and find that the average cost is $121.33 with a standard deviation of $18.046. At the α = 0.05 significance level, determine if there is enough evidence to reject the claim. What is the decision for this hypothesis test? You were told that the mean daily cost of a hotel room in downtown St. Louis is $120. You will be needing to rent a hotel room there in the near future and you want to find the best rate. You randomly select a sample of 18 hotel rooms and find that the average cost is $121.33 with a standard deviation of $18.046. At the α = 0.05 significance level, determine if there is enough evidence to reject the claim. What is the decision for this hypothesis test? Reject the null because the test statistic is in the critical region and the…The College Board reports that the scores on the math SAT were normally distributed with a mean of 525. A random sample of 15 students at your high school had a mean of 550 and a sample standard deviation of 105. What values of the sample mean would lead to rejection of the null hypothesis at the 0.01 level of significance?The accounts of a corporation show that on average, accounts payables are $125 with standard deviation of $25. An auditor checked a random sample of 20 accounts whose mean was $129. Assume that the population distribution is normal. Test the null hypothesis that the mean payables are $125 against a two- sided alternative at 5% significance level. State the null and the alternative hypothesis and comment whether its a one tail or two tail test? If one tail then right or left tail test? (write your answer as one tail right tail test/ one tail left tail test/ two tail test) Identify the critical value. Ans in two decimal places. What is the calculated value? Ans in two decimal places Write the decision rule and identify whether the condition holds. (write answer as condition holds/ condition does not hold) Give final decision (write answer as reject null/ do not reject null)
- In the past, the mean running time for a certain type of flashlight battery has been 8.5 hours. The manufacturer has introduced a change in the production method and wants to perform a hypothesis test to determine whether the mean running time has changed as a result. A. Lower-tailed B. Upper-tailed C. Two-sided O A B O CIn the past, the time for Jeff's journey to work had mean 45.7 minutes and standard deviation 5.6 minutes. This year he is trying a new route. In order to test whether the new route has reduced his journey time, Jeff finds the mean time for a random sample of 30 journeys using the new route. He camies out a hypothesis test at the 2.5% significance level. Jeff assumes that, for the new route, the joumey time has a nomal distribution with standard deviation 5.6 minutes. (a) State appropriate null and alternative hypotheses for the test. (b) Determine the rejection region for the test.In a study of computer use, 1000 randomly selected Canadian Internet users were asked how much time they spend using the Internet in a typical week. The mean of the sample observations was 12.8 hours. (a) The sample standard deviation was not reported, but suppose that it was 6 hours. Carry out a hypothesis test with a significance level of 0.05 to decide if there is convincing evidence that the mean time spent using the Internet by Canadians is greater than 12.6 hours. (Use a statistical computer package to calculate the P-value. Round your test statistic to two decimal places and your P-value to four decimal places.) t=P-value= State the conclusion in the problem context. Reject H0. We have convincing evidence that the mean weekly time spent using the Internet by Canadians is greater than 12.6 hours.Do not reject H0. We have convincing evidence that the mean weekly time spent using the Internet by Canadians is greater than 12.6 hours. Reject H0. We do not have convincing…