In this discussion, you will learn how to test a hypothesis. That means you will be looking at data to see if you can prove or disprove a claim. As in the previous chapters most of the calculations are done by StatCrunch, but you need to decide which distribution to use, what values to plug in, and which options to choose. These exercises are designed to help you practice these tasks. Here’s a brief explanation of each task. We need to state the null and alternative hypotheses (H0 and H1):We need to determine the value that is a parameter and the value that is a statistic:Based on the hypotheses in Part 1 and the values in Part 2, decide what distribution to use (Note:This is similar to deciding the type of the confidence interval): The null-hypothesis is always the previously accepted value for the parameter and is always written as an equation,for example: or or. The alternative hypothesis, which is never an equation, is based on the hypothesis stated in the problem, for example: or or. Here are the possible parameter and statistic values that you may have in a problem: (Population proportion, sample proportion, sample size, population size, population mean, sample mean, population standard deviation, sample standard deviation). If the hypothesis is about the proportion (and the conditions on page 437 are met), then we use the Proportion Stats in StatCrunch. If the hypothesis is about ,then we use either the T-Stat or the Z-Stat. Z-Stat is used when we know , which is rarely true. Most of the time we only know “S”. In that case, as long as the population is known to be normal or if it isn’t normal (), then we use the T-Stats in StatCrunch. If the hypothesis is about , then we use the Variance Stats option in StatCrunch. You Try It! – Foreach of the following examples, perform the three tasks described above: State H0 and H1Find the values for:if they are given or are needed.State which StatCrunch menu needs to be used. Read the example cases on the next page… A shipping firm suspects that the mean life of a certain brand of tire used by its trucks is less than 40,000 miles. To check the claim, the firm randomly selects and tests 18 of these tires and gets a mean lifetime of 39,300 miles with a standard deviation of 1200 miles. At α = 0.05, test the shipping firm's claim. Round the test statistic to the nearest thousandth. A brokerage firm needs information concerning the standard deviation of the account balances of its customers. From previous information it was assumed to be $250. A random sample of 61 accounts was checked. The standard deviation was $286.20. At α = 0.01, test the firm's assumption. Assume that the account balances are normally distributed. A survey claims that 9 out of 10 doctors (i.e., 90%) recommend brand X for their patients who have children. To test this claim against the alternative that the actual proportion of doctors who recommend brand X is less than 90%, a random sample of 100 doctors results in 92 who indicate that they recommend brand X. Test the claim at α = 0.01. A local juice manufacturer distributes juice in bottles labeled 12 ounces. A government agency thinks that the company is cheating its customers. The agency selects 20 of these bottles, measures their contents, and obtains a sample mean of 11.7 ounces with a standard deviation of 0.7 ounce. Use a 0.01 significance level to test the agency's claim that the company is cheating its customers. A local group claims that the police issue at least 60 parking tickets a day in their area. To prove their point, they randomly select two weeks. Their research yields the number of tickets issued for each day. The data are listed below. At α = 0.01, test the group's claim. Use StatCrunch to calculate the relevant statistics. A statistics professor at an all-men's college determined that the standard deviation of men's heights is 2.5 inches. The professor then randomly selected 41 female students from a nearby all-female college and found the standard deviation to be 2.9 inches. Test the professor's claim that the standard deviation of female heights is greater than 2.5 inches. Use α = 0.01. 20, 48, 41, 68, 69, 70, 57, 60, 83, 32, 60, 72, 58, 63

Choose any variable you want to measure (e.g., cups of coffee consumed per week, minutes of screen time per day, etc.) and collect data from a sample of your choice (e.g., children, adults, college students, family members, etc.) of minimum size n=10. Complete the following: What specific variable are you measuring and what is your sample of interest? Is your variable continuous or discrete? Which scale of measurement is your variable categorized as (nominal, ordinal, interval, or ratio)? Calculate the mean, median, and mode for your sample. Draw a scatterplot or a histogram (whichever is appropriate for your data). You can use a computer program to create this graph, or simply hand-draw it and include a picture (e.g., taken with your phone) within your document.