Topic: Hypothesis Testing

Subject: Statistics and Probability

With solution needed

1. Each of the following situations requires a significance test about a population mean State the appropriate null hypothesis H0 and alternative hypothesis Ha in each case:

d. Your company sells exercise clothing and equipment on the Internet. To design the clothing, you collect data on the physical characteristics of your different types of customers. We take a sample of 24 male runners and find their mean weight to be 61.79 kilograms. Assume that the population standard deviation is o = 4.5. Calculate a 95% confidence interval for the mean weight of all such runners: Based on this confidence interval, does a test of Ho: u = 61.3 kg HA: p x 61.3 kg reject Ho at the 5% significance level? . Carry out the hypothesis test in 3 to verify your answer: c. Last year the government made a claim that the average income of the American people was $33,950. However, a sample of 50 people taken recently showed an average income of $34,076 with a population standard deviation of $324. Is the government's estimate too low? Conduct a significance test to see if the true mean is more than the reported average. Use an alpha = 0.01.f. An environmentalist collects a liter of water from 45 different locations along the banks of a stream. He measures the amount of dissolved oxygen in each specimen. The mean oxygen level is 4.62 mg, with the overall standard deviation of 0.92. A water purifying company claims that the mean level of oxygen in the water is 5 mg. Conduct a hypothesis test with alpha = 0.001 to determine whether the mean oxygen level is less than 5 mg. g. A bus company advertised a mean time of 150 minutes for a trip between two cities. A consumer group had reason to believe that the mean time was more than 150 minutes. A sample of 40 trips showed a mean *= 153 minutes and a standard deviation s=7.5 minutes. At the .05 level of significance, test the consumer group's belief