A supplier sells ropes. He claims that the ropes have a mean strength of 34 pounds and a variance of 64 pounds. A random sample of 32 ropes selected from a shipment yields a mean strength of 31 pounds. Could the claim of the supplier be rejected at 0.05 level?
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A supplier sells ropes. He claims that the ropes have a
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- A production engineer wants to determine if two assembly lines are producing the same mean number of units daily. To test this: a sample of 10 days on line A reveals a mean of 110 units with a variance of 200 a sample of 15 days on line B reveals a mean of 100 units with a variance of 150. Set up hypotheses and perform the appropriate test to resolve this question. Fully interpret your results.A parenting magazine reports that the average amount of wireless data used by teenagers each month is 10 Gb. For her science fair project, Ella sets out to prove the magazine wrong. She claims that the mean among teenagers in her area is less than reported. Ella collects information from a simple random sample of 4 teenagers at her high school, and calculates a mean of 8.4 Gb per month with a standard deviation of 2.2 Gb per month. Assume that the population distribution is approximately normal. Test Ella's claim at the 0.05 level of significance. Step 1 of 3: State the null and alternative hypotheses for the test. Fill in the blank below. Η :μ H₂H = 10 10For a study conducted by the research department of a pharmaceutical company, 245 randomly selected individuals were asked to report the amount of money they spend annually on prescription allergy relief medication. The sample mean was found to be $17.80 with a standard deviation of $4.30. A random sample of 225 individuals was selected independently of the first sample. These individuals reported their annual spending on non-prescription allergy relief medication. The mean of the second sample was found to be $18.20 with a standard deviation of $3.60. As the sample sizes were quite large, it was assumed that the respective population standard deviations of the spending for prescription and non-prescription allergy relief medication could be estimated as the respective sample standard deviation values given above. Construct a 90% confidence interval for the difference H₁ H₂ between the mean spending on prescription allergy relief medication (₁) and the mean spending on non-prescription…
- The township of Middleton sets the speed limit on its roads by conducting a traffic study and determining the speed (to the nearest 5 miles per hour) at which 80% of the drivers travel at or below. A study was done on Brown's Dock Road that indicated driver's speeds follow a normal distribution with a mean of 36.25 miles per hour and a variance of 6.25. (a) What should the speed limit be? (b) What percentage of the drivers travel below the speed limit?A sample of 79 female workers and another sample of 51 male workers from a state produced mean weekly earnings of $728.22 for the females and $761.88 for the males. Suppose that the population standard deviations of the weekly earnings are $ 75.84 for all females and $ 102.10 for all males. The null hypothesis is that the mean weekly earnings are the same for females and males, while the alternative hypothesis is that the mean weekly earnings for females is less than the mean weekly earnings for males. Derive the corresponding 95% confidence interval, rounded to two decimal places, for the difference between the mean weekly earnings for all female and male workers in this state. to iA production engineer wants to determine if two assembly lines are producing the same mean number of units To test this: a sample of 10 days on line A reveals a mean of 110 units with a variance of 200 a sample of 15 days on line B reveals a mean of 100 units with a variance of 150. 1. Set up hypotheses and perform the appropriate test to resolve this question. Fully interpret your results.
- A sample of 76 female workers and another sample of 48 male workers from a state produced mean weekly earnings of $743.50 for the females and $777.63 for the males. Suppose that the population standard deviations of the weekly earnings are $80.05 for the females and $88.68 for the males. The null hypothesis is that the mean weekly earnings are the same for females and males, while the alternative hypothesis is that the mean weekly earnings for females is less than the mean weekly earnings for males. Directions: • Label your answers with the correct statistical symbols. • If you use the Ti, identify which function and values you used to calculate. If you solve by hand, show all steps. 2.1. Derive the corresponding 95% confidence interval, rounded to two decimal places, for the difference between the mean weekly earnings for all female and male workers in this state. 2.2. What is the point estimate? 2.3. What is E? 2.5. The significance level for the test is 1%. What is/are the critical…2. Suppose the weight of fish caught from the Santa Monica Pier is normally distributed. From a random sample of 20 recently caught fish, the sample mean is found to be 22.0 ounces and the sample variance is found to be 25.0 ounces. The Fish and Wildlife Department states that the true mean weight is 24.0 ounces. Fishermen claim that due to increased pollution in the bay, the true mean weight is less than 24.0 ounces. Test the claim of the Fish and Wildlife Department at α = 0.05 (or 5%). [14 pts total] What is the null hypothesis? [2 pt] a. Ο μ = 24 Ο μ 24 b. What is the one-sided alternative hypothesis? [2 pt] μ = 24 Ο μ 24 μ = 24 Draw a t-distribution for the alternative hypothesis. Label the mean and shade in the area(s) where you can reject the null hypothesis. [4 pts] d. Calculate and report the appropriate test statistic (3 sig figs) [4 pts] and make your conclusion [2 pts] Reject the null hypothesis Value of test statistic: Fail to reject the null hypothesis 2A basketball coach believes that the variance of the heights of adult male basketball players is different from the variance of heights for the general population of men. The sample variance of heights, measured in inches, for a random sample of 19 basketball players is 14.22. The sample variance for a random sample of 18 other men is 34.49. Assume that both population distributions are approximately normal and test the coach's claim using a 0.10 level of significance. Does the evidence support the coach's claim? Let male basketball players be Population 1 and men in general be Population 2. Step 3 of 3: Draw a conclusion and interpret the decision.
- A parenting magazine reports that the average amount of wireless data used by teenagers each month is 10 Gb. For her science fair project, Ella sets out to prove the magazine wrong. She claims that the mean among teenagers in her area is less than reported. Ella collects information from a simple random sample of 4 teenagers at her high school, and calculates a mean of 8.4 Gb per month with a standard deviation of 2.2 Gb per month. Assume that the population distribution is approximately normal. Test Ella's claim at the 0.05 level of significance. Step 3 of 3: Draw a conclusion and interpret the decision. Answer Tables Keypad Keyboard Shortcuts We reject the null hypothesis and conclude that there is sufficient evidence at a 0.05 level of significance that the average amount of wireless data used by teenagers each month is less than 10 Gb. We reject the null hypothesis and conclude that there is insufficient evidence at a 0.05 level of significance that the average amount of wireless…1) The mean and variance of a sample of 25 data items are 78 and 100, respectively. Use Chebyshev's theorem to describe the distribution of the data.A coin-operated coffee machine made by BIG Corporation was designed to discharge a mean of 7.0 ounces of coffee per cup. If it dispenses more than that on average, the corporation may lose money, and if it dispenses less, the customers may complain. Believing that the mean amount of coffee dispensed by the machine, u, is greater than 7.0 ounces, BIG plans to do a statistical test of the claim that the machine is working as designed. Technicians gather a random sample of fill amounts and find that the mean of the sample is 7.4 ounces and that the standard deviation is 0.3 ounces. 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? H: u is ? Η: μs7 In the context of this test, what is a Type I error? v the hypothesis that u is ? ? v. A Type I error is ? v|? when, in fact, u is ? Suppose that BIG decides to reject the null hypothesis. What sort of error might it be making? ?
