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1. A new breakfast cereal is test-marketed for 1 month at stores of a large supermarket chain. The results for a sample of 16 stores indicate average sales of $1,200 with a standard deviation of $180. Assuming a
2. If the
3. A machine being used for packaging seedless golden raisins has been set so that on average, 15 ounces of raisins will be packaged per box. The quality control engineer wishes to test the machine setting and selects a sample of 30 consecutive raisin packages filled during the production process. Their weights are recorded as follows: 15.2 15.3 15.1 15.7 15.3 15.0 15.1 14.3 14.6 14.5 15.0 15.2 15.4 15.6 15.7 15.4 15.3 14.9 14.8 14.6 14.3 14.4 15.5 15.4 15.2 15.5 15.6 15.1 15.3 15.1 At the 5% level of significance, is there evidence that the mean weight per box is different from 15 ounces? Use the 5-step classical rejection region critical value decision rule for this problem. You may use the TI-84 t-test option to calculate the test statistics (tStat). For the rejection region approach recall that we look up the tcritical on the t table, tα,n-1 for a 1 tail and tα/2,n-1 for a 2 tail test. State the meaning of µ, then list the 5 steps. If you reject Ho, construct a (1-α)% CI for µ, and state what we think µ is now after you reject Ho.
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- A random sample of 90 eighth grade students' scores on a national mathematics assessment test has a mean score of 288. This test result prompts a state school administrator to declare that the mean score for the state's eighth graders on this exam is more than 280. Assume that the population standard deviation is 36. At α = 0.08, is there enough evidence to support the administrator's claim? Complete parts (a) through (e). (a) Write the claim mathematically and identify Ho and H₂. Choose the correct answer below. A. Ho: μ = 280 (claim) Ha:μ>280 Ho:μ≤280 Ha: μ> 280 (claim) B. Ho: μ = 280 P-value = (b) Find the standardized test statistic z. z = 2.11 (Round to two decimal places as needed.) (c) Find the P-value. E. Ho: μ≤280 (claim) Ha:μ>280 Ha: μ> 280 (claim) (Round to three decimal places as needed.) C. Ho: μ ≥280 (claim) Ha:μ< 280 F. Ho: μ< 280 H₂:μ ≥280 (claim)arrow_forwardA random sample of 82 eighth grade students' scores on a national mathematics assessment test has a mean score of 286. This test result prompts a state school administrator to declare that the mean score for the state's eighth graders on this exam is more than 280. Assume that the population standard deviation is 38. At α = 0.05, is there enough evidence to support the administrator's claim? Complete parts (a) through (e). (a) Write the claim mathematically and identify Ho and H₂. Choose the correct answer below. O A. Ho: ≤280 (claim) H₂:μ>280 O D. Ho: μ≤280 Ha: μ> 280 (claim) B. Ho: μ280 OF. Ho: μ = 280 H₂: µ>280 (claim)arrow_forwardIn a sample of 12 randomly selected high school seniors, the mean score on a standardized test was 1182 and the standard deviation was 161.6.Further research suggests that the population mean score on this test for high school seniors is 1012. Does the t-value for the original sample fall between −t0.95 and t0.95? Assume that the population of test scores for high school seniors is normally distributed. What is The t-value? And does or does not it not fall between −t0.95 and t0.95 because t0.95=? (Round to two decimal places as needed.)arrow_forward
- Q1: A researcher was interested in the effect of exercise on stress levels. For the general population, the distribution of the Stress Battery Scale scores is normal with the mean of µ = 25 and the standard deviation of σ = 5. A sample of n = 100 participants was asked to exercise for three weeks and then reported their stress levels. The sample mean was ?X = 23. Conduct a hypothesis test and determine the effect of exercise. Use the two-tailed test α = .01 1.Type the null and research hypotheses in complete sentences. 2.Cut off points 3.Standard error and z-score -show your computation process 4.Your conclusion thoroughly.arrow_forwardA manufacturer bonds a plastic coating to a metal surface. A random sample of nine observations on the thickness of this coating is taken from a week's output and the thickness (in millimeters) of these observations are shown below. Assuming normality, find a 90 % confidence interval for the population variance. 19.7 20.5 Click the icon to view a table of lower critical values for the chi-square distribution. Click the icon to view a table of upper critical values for the chi-square distribution. 21.8 18.2 Find the 90% confidence interval. 0<²0 (Round to four decimal places as needed.) 21.6 SCIOD 19.3 19.7 20.2 20.7arrow_forwardIn a random sample of 8 cell phones, the mean full retail price was $549.30 and the standard deviation was $182.00. Further research suggests that the population mean is $425.14. Does the t-value for the original sample fall between - to 95 and to 95? Assume that the population of full retail prices for cell phones is normally distributed. The t-value of t = fall between - to 95 and to 95 because to 95 (Round to two decima d.) does not doesarrow_forward
- An obstetrician read that a newborn baby loses on average 7 ounces in the first two days of his or her life. He feels that in the hospital where he works, the average weight loss of a newborn baby is less than 7 ounces. A random sample of 30 newborn babies has a mean weight loss of 6.4 ounces. The population standard deviation is 1.6 ounces. Is there enough evidence at =α0.01 to support his claim? Assume that the variable is normally distributed. Use the critical value method with tables. hello the question askas to find the critical value compute the test value and select the hypothesisarrow_forwardA researcher would like to test the effect of the herbal remedies on memory ability in healthy adults. For a general population, memory scores from the test are positively skewed with a mean of μ = 80 and a standard deviation of σ = 18. A researcher obtains a sample of n = 16 participants and has each person take the herbal supplements every day for 90 days. The sample mean is M = 84. Can you conclude that the herbal remedies have an effect on memory? Use α = .01 and show every step of hypothesis testarrow_forwardThe heights of people in a certain population are normally distributed with a mean of 68 inches and a standard deviation of 4.4 inches. Suppose that a normal model applies. The model that correctly shows the 68-95-99.7 rule (empirical rule) for tree diameter is model: B C A About 68% of heights fall in the range described by option between 59.2 and 76.8. below 63.6. between 54.8 and 81.2. between 63.6 and 72.4. above 72.4. What percent of people in this population have heights below 59.2? %_arrow_forward
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