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## 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 therivalâ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 rivalâs store spend more than those at CostcoCustomers at the rivalâs store do not spend more than those at Costco

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