The following distributions are for that suggested by null hypothesis of Z-test and two of those suggested by the alternative hypothesis (HAI and HA2). Which of the following is correct
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- A two-tailed test is performed at 95% confidence. The p-value is determined to be 0.0478. The null hypothesis must be rejected should not be rejected could be rejected, depending on the sample size has been designed incorrectlyAn improved battery is being developed by a start-up company, which will be sent to the smartphones manufacturer. Suppose that the charging time for the old battery is normally distributed with a mean on 45 minutes, while the charging time for the new battery is normally distributed with a mean of 30 minutes. Given the standard deviation of the old battery is 20 minutes and the new battery is 30 minutes, respectively. Twenty random samples of both batteries were tested. Find the probability of sample of the new battery is better than the old one.The test statistic for a two tailed hypothesis test on a sample of 18 is 2.639. Find an interval for which the p-value lies.
- Ten (10) of your most trustworthy friends take a polygraph test. The odds of a trustworthy person failing the polygraph test is 0.15. Let the random variable X be the number of your friends that fail the polygraph test, What is the probability that less than 4 of them failed? The weight of goats at a farm is normally distributed with a mean of 60 kg and a standard deviation of 10 kg. A truck used to transport goats can only accommodate not more than 650 kg. If 10 goats are selected at random from the population, what is the probability that the total weight exceeds the maximum weight?The manager of a computer retail store is concerned that his suppliers have been giving him laptop with lower than average quality. His research shows that replacement times for the model laptop of concern are normally distributed with a mean of 3.6 years and a standard deviation of 0.5 years. He then randomly selects records on 44 laptop sold in the past and finds that the mean replacement time is 3.4 years. Find the probability that 44 randomly selected laptops will have a mean replacement time of 3.4 years or less. b] Based on the result, above does it appear that the computer store has been given laptops of lower than average quality C} Please also do explain how to solve using ExcelTwo treatments for a new infectious disease have been developed to reduce hospitalizations. Each treatment was given to different groups of patients. Treatment 1 was given to 65 people. Subjects of treatment 1 had a mean hospital stay of 5.6 days with a standard deviation of 2.6 days. Treatment 2 was given to 54 people. Subjects of treatment 2 had a mean hospital stay of 8.4 days with a standard deviation of 3.0 days. Use the method of hypothesis testing to test the claim that the mean time in the hospital for treatment 1 is shorter than the mean time in the hospital for treatment 2 assuming a 0.05 significance level. (a) List the null and alternative hypotheses for this test. (b) Compute the value of the test statistic (c) Determine the rejection region.(d) Determine whether or not we can reject the null hypothesis.
- Answer the given word problem by performing the test of hypothesis using t- test with two unequal sample means and standard deviations. A teacher wishes to find out if the proposed method of teaching Statistic is more effective than the existing. Two groups of approximately equal intelligence were randomly selected. From one group, the teacher selected 10 students for the proposed method of teaching. From the second group, the teacher selected another 9 students for existing method. After 2 months of teaching, same 30 item test was administered to the two groups. Below are the summary of the values used. Method Proposed Existing N 10 N2 = 9 X = 24.27 X = 21.07 S = 4.98 S2 5.21Tata Motors, Ltd., purchases computer process chips from two suppliers, and the company is concerned about the percentage of defective chips. A review of the records for each supplier indicates that the percentage defectives in consignments of chips follow normal distributions with the means and standard deviations given in the following table. The company is particularly anxious that the percentage of defectives in a consignment not exceed 5% and wants to purchase from the supplier that’s more likely to meet that specification. Which supplier should be chosen? Mean Standard Deviation Supplier A Supplier B 4.4 4.2 0.4 0.6In 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.
- BIG Corporation advertises that its light bulbs have a mean lifetime, u, of 3000 hours. Suppose that we have reason to doubt this claim and decide to do a statistical test of the claim. We choose a random sample of light bulbs manufactured by BIG and find that the mean lifetime for this sample is 3160 hours and that the sample standard deviation of the lifetimes is 600 hours. Based on this information, answer the questions below. What are the null hypothesis (H.) and the alternative hypothesis (H,) that should be used for the test? Ho: u is ? H: u is ? In the context of this test, what is a Type I error? A Type I error is ? v the hypothesis that u is? when, in fact, u is ? Suppose that we decide to reject the null hypothesis. What sort of error might we be making? ?Which of the following is the research hypothesis of one-tailed dependent t-test expecting to see a significant decrease in the observed scores? A. mean(posttest) < mean(pretest) B. mean(posttest) = mean(pretest) C. mean(posttest) > mean(pretest) D. mean(posttest) ≠ mean(pretest)