Exam 8: Hypothesis Testing

Use the given information to find the P-value. Also, use a 0.05 significance level and state the conclusion about the null hypothesis (reject the null hypothesis or fail to reject the null hypothesis). -The test statistic in a left-tailed test is z = -2.05.

Use the given information to find the P-value. Also, use a 0.05 significance level and state the conclusion about the null hypothesis (reject the null hypothesis or fail to reject the null hypothesis). -The test statistic in a right-tailed test is z = 1.43.

In a sample of 47 adults selected randomly from one town, it is found that 9 of them have been exposed to a particular strain of the flu. Find the P-value for a test of the claim that the proportion of all adults in the town that have been exposed to this strain of the flu is 8%.

Use the traditional method to test the given hypothesis. Assume that the population is normally distributed and that the sample has been randomly selected. -A manufacturer uses a new production method to produce steel rods. A random sample of 17 steel rods resulted in lengths with a standard deviation of 2.1 cm. At the 0.10 significance level, test the claim that the new production method has lengths with a standard deviation different from 3.5 cm, which was the standard deviation for the old method.

Assume that a simple random sample has been selected from a normally distributed population. Find the test statistic, P-value, critical value(s), and state the final conclusion. -Test the claim that for the adult population of one town, the mean annual salary is given by $\mu = \$ 30,000$ . Sample data are summarized as $n = 17 , \bar { x } = \$ 22,298$ , and $s = \$ 14,200$ . Use a significance level of $\alpha = 0.05$ .

Find the P-value for the indicated hypothesis test. -A nationwide study of American homeowners revealed that 65% have one or more lawn mowers. A lawn equipment manufacturer, located in Omaha, feels the estimate is too low for households in Omaha. Find the P-value for a test of the claim that the proportion with lawn mowers in Omaha is higher than 65%. Among 497 randomly selected homes in Omaha, 340 had one or more lawn Mowers.

Jenny is testing a claim about a population mean. The hypotheses are as follows. $\mathrm { H } _ { 0 } : \mu = 50$ $\mathrm { H } _ { 1 } : \mu > 50$ She selects a simple random sample and finds that the sample mean is 54.2. She then does some calculations and is able to make the following statement: If H0 were true, the chance that the sample mean would have come out as big ( or bigger) than 54.2 is 0.3. What name is given to the value 0.3? Do you think that she should reject the null hypothesis? Why or why not?

Assume that a hypothesis test of the given claim will be conducted. Identify the type I or type II error for the test. -The principal of a school claims that the percentage of students at his school that come from single-parent homes is 16%. Identify the type II error for the test.

Under what conditions do you reject $\mathrm { H } _ { 0 }$ ? Discuss both the traditional and the P-value approach.

A manufacturer makes ball bearings that are supposed to have a mean weight of 30 g. A retailer suspects that the mean weight is actually less than 30 g. The mean weight for a random sample of 16 ball bearings is 29.2 g with a standard deviation of 4.2 g. At the 0.05 significance level, test the claim that the sample comes from a population with a mean weight less than 30 g. Use the traditional method of testing hypotheses.

Assume that a hypothesis test of the given claim will be conducted. Identify the type I or type II error for the test. -The owner of a football team claims that the mean attendance at games is over 85,700, and he is therefore justified in moving the team to a city with a larger stadium. Identify the type II error for the test.

Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim. -A nationwide study of American homeowners revealed that 64% have one or more lawn mowers. A lawn equipment manufacturer, located in Omaha, feels the estimate is too low for households in Omaha. Can the value 0.64 be rejected if a survey of 490 homes in Omaha yields 331 with one or more lawn mowers? Use $\text { Use } \alpha = 0.05$

What do you conclude about the claim below? Do not use formal procedures or exact calculations. Use only the rare event rule and make a subjective estimate to determine whether the event is likely. Claim: An employee of a company is equally likely to take a sick day on any day of the week. Last year, the total number of sick days taken by all the employees of the company was 143. Of these, 52 were Mondays, 14 were Tuesdays, 17 were Wednesdays, 17 were Thursdays, and 43 were Fridays.

Express the null hypothesis and the alternative hypothesis in symbolic form. Use the correct symbol (µ, p, σ) for the indicated parameter. -A psychologist claims that more than 3.2 percent of the population suffers from professional problems due to extreme shyness. Use p, the true percentage of the population that suffers from extreme shyness.

Find the P-value for the indicated hypothesis test. -A medical school claims that more than 28% of its students plan to go into general practice. It is found that among a random sample of 130 of the school's students, 32% of them plan to go into general practice. Find the P-value for a test of the school's claim.

Explain how to determine if a hypothesis test is one-tailed or two-tailed and explain how you know where to shade the critical region. Give an example for each which includes the claim, the hypotheses, and the diagram with the critical region shaded.

Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim -In a clinical study of an allergy drug, 108 of the 202 subjects reported experiencing significant relief from their symptoms. At the 0.01 significance level, test the claim that more than half of all those using the drug experience relief.

Provide an appropriate response -Compare the steps in the traditional method of hypothesis testing with the steps in the P-value method of hypothesis testing. How are they alike and how are they different? Traditional Method P-value Method Comparison

Provide an appropriate response -A simple random sample of 15-year old boys from one city is obtained and their weights (in pounds) are listed below. Use a 0.01 significance level to test the claim that these sample weights come from a population with a mean equal to 150 lb. Assume that the standard deviation of the weights of all 15-year old boys in the city is known to be 16.4 lb. Use the traditional method of testing hypotheses. 144 140 161 151 134 189 157 144 175 127 164

Assume that the data has a normal distribution and the number of observations is greater than fifty. Find the critical z value used to test a null hypothesis. - $\alpha = 0.08 ; \mathrm { H } _ { 1 }$ is $\mu \neq 3.24$