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According to the Insurance Information Institute, the mean expenditure for auto insurance in the United States was $774 in 2002. An insurance sales person believes that the mean expenditure for auto insurance is different now. He obtains a random sample of 35 auto insurance policies and determines the mean expenditure to be $815 with a standard deviation of $88.31. Is there sufficient evidence to conclude that the mean expenditure for auto insurance is different from the 2002 amount at the α = 0.10 level of significance?What is the decision rule (do you reject the null and conclude the alternative or do you fail to reject the null)? Please sure to state why.

An ABC News poll in April 2007 of a random sample of 1002 adults nationwide asked about various measures the government could take to try to reduce future global warming (www.pollingreport.com/enviro.htm). When asked whether the government should increase taxes on gasoline so people either drive less or buy cars that use less gas, 681 people said no. Test, at the 0.01 level of significance, the claim that the majority (more than 50%) of U.S. adults believe that the government should not increase taxes on gasoline to help reduce future global warming.State the value of the test statistic. Round to two decimal places.

The box plots below illustrate the distribution of graduation rates for a sample of public universities and for a sample of private universities. Based on the box plots, which of the following statements must be TRUE?

A journal article reports that 34% of American fathers take no responsibility for child care. A researcher claims that the figure is higher for fathers in a particular town. A random sample of 233 fathers from this town yielded 96 who did not help with child care. The sample data produces a p-value = 0.0102. What is the conclusion of the test if the level of significance is 0.05?

The following is a printout involving the variable SMOKE (Do you smoke?) from MAT 131 Student Survey for a randomly selected semester. Assume that this is a representative sample from the population of all students taking Statistics I at Cincinnati State.Tally for Discrete Variables: SMOKE                         SMOKE  Count                           No      169                           Yes      21                           N =     190 Compute the best estimate for the proportion of all students taking Statistics I at Cincinnati State that smoke. Round to three decimal places.

Experiments on animal learning often measure how long a mouse takes to get through a maze. For one particular maze, the true mean time is 18 seconds. A researcher thinks that a loud noise will help the mice to complete the maze faster. She measures the average time, x-bar, required for 10 mice to complete the maze when the loud noise is played. Which is a suitable null hypothesis in this situation?

Gasoline pumped from a supplier’s pipeline is supposed to have an octane rating of 87.5. For 13 consecutive days, a liter of gas from the pipeline was obtained and analyzed. The resulting octane readings for these 13 days are given below:88.6     86.4     87.2     88.4     87.2     87.6     86.8     86.1     87.4     87.3     86.4     86.6     87.1Here is the data set in StatCrunch. The supplier wants to test the claim that the octane reading from the pipeline has a true mean that is less than 87.5 at the 5% level of significance.Are the results of the test statistically significant?

Gasoline pumped from a supplier’s pipeline is supposed to have an octane rating of 87.5. For 13 consecutive days, a liter of gas from the pipeline was obtained and analyzed. The resulting octane readings for these 13 days are given below:88.6     86.4     87.2     88.4     87.2     87.6     86.8     86.1     87.4     87.3     86.4     86.6     87.1Here is the data set in StatCrunch. The supplier wants to test the claim that the octane reading from the pipeline has a true mean that is less than 87.5 at the 5% level of significance. State the null and alternative hypothesis for this situation and the type of tail.

Public Policy Polling (PPP), a reputable polling company, asked the following question in a previous Halloween-eccentric public opinion poll:“If zombies took over the world and human civilization collapsed, how long do you think you could survive: less than one week, less than one month, less than six months, less than one year, or more than a year?” Of the 1,200 likely voters who were asked this question, 324 said “Less than one week”. Construct a 99% confidence interval for the true population percentage of likely voters who said that they would survive a zombie apocalypse for less than one week. Round to three decimal places.

A local eat-in pizza restaurant wants to investigate the possibility of starting to deliver pizzas. The owner of the store has determined that home delivery will be successful if the average time spent on the deliveries does not exceed 30 minutes. The owner has randomly selected 50 customers and has delivered pizzas to their homes in order to test if the mean delivery time does not exceed 30 minutes. Suppose the p-value for the test was found to be 0.0287. State the correct conclusion at the significance level of 0.01.