Statistics- The screening process for detecting a rare disease is not perfect

Statistics- The screening process for detecting a rare disease is not perfect

Statistics- The screening process for detecting a rare disease is not perfect

1. The screening process for detecting a rare disease is not perfect. Researchers have developed ablood test that is considered fairly reliable. It gives a positive reaction in 95.0% of the people who havethat disease. However, it erroneously gives a positive reaction in 2.5% of the people who do not have thedisease. Answer the following questions using the null hypothesis as "the individual does not have thedisease."a. What is the probability of Type I error? (Round your answer to 3 decimal places.)Probabilityb. What is the probability of Type II error? (Round your answer to 3 decimal places.)Probability2. Customers at Costco spend an average of $130 per trip (The Wall Street Journal, October 6, 2010).One of Costco’s rivals would like to determine whether its customers spend more per trip. A survey of thereceipts of 25 customers found that the sample mean was $135.25. Assume that the population standarddeviation is $10.50 and that spending follows a normal distribution. Use Table 1.a. Specify the appropriate null and alternative hypotheses to test whether average spending at therival’s store is more than $130.H0: μ ≤ 130; HA: μ > 130H0: μ = 130; HA: μ ≠ 130H0: μ ≥ 130; HA: μ < 130b-1. Calculate the value of the test statistic. (Round your intermediate calculations to 4 decimalplaces and final answer to 2 decimal places.)Test statisticb-2. Calculate the p-value. (Round your answer to 4 decimal places.)p-valuec. At the 5% significance level, what is the conclusion based on the p-value approach?Reject H0 since the p-value is greater than α.Reject H0 since the p-value is smaller than α.Do not reject H0 since the p-value is greater than α.Do not reject H0 since the p-value is smaller than α.d-1. Calculate the critical value. (Round your answer to 2 decimal places.)Critical valued-2. At the 5% significance level, what is the conclusion based on the critical value approach?Customers at the rival’s store spend more than those at CostcoCustomers at the rival’s store do not spend more than those at Costco

 

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