Exam 8: Hypothesis Testing

Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim -Sam wanted to test a claim about the mean of a population whose standard deviation was unknown. He picked a simple random sample of size 20 from the population. Lou wanted to test a claim about a mean of a different population whose standard deviation was known. He picked a simple random sample of size 22 from that population. George said that Sam would need to determine whether his sample was from a normally distributed population because the population standard deviation was unknown. He said that Lou would not need to do this since for his test the population standard deviation was known. Is George right?

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 machine dispenses a liquid drug into bottles in such a way that the standard deviation of the contents is 81 milliliters. A new machine is tested on a sample of 24 containers and the standard deviation for this sample group is found to be 26 milliliters. At the 0.05 level of significance, test the claim that the amounts dispensed by the new machine have a smaller standard deviation.

Suppose that you wish to test a claim about a population mean. Which distribution should be used given that the sample is a simple random sample, ? is unknown, n = 15, and the population is not normally distributed?

Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and finalconclusion that addresses the original claim. -A poll of 1068 adult Americans reveals that 48% of the voters surveyed prefer the democratic candidate for the presidency. At the 0.05 level of significance, test the claim that at least half of all voters prefer the Democrat.

Formulate the indicated conclusion in nontechnical terms. Be sure to address the original claim. -Carter Motor Company claims that its new sedan, the Libra, will average better than 30 miles per gallon in the city. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is to reject the null hypothesis, state the conclusion in nontechnical terms.

Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim -David wants to test a claim about a population mean. The population standard deviation is unknown, the sample is a simple random sample of size 20, and the population is normally distributed. In this case, the t-test should be used since ? is unknown. If David incorrectly uses the normal distribution instead of the t-distribution, will he obtain a P-value that is too big or too small? Explain your thinking. Will he be more likely or less likely to reject the null hypothesis than if had correctly used the t-distribution?

Assume that a simple random sample has been selected from a normally distributed population and test the given claim. Use either the traditional method or P-value method as indicated. Identify the null and alternative hypotheses, test statistic, critical value(s) or P-value (or range of P-values) as appropriate, and state the final conclusion that addresses the original claim. -A test of sobriety involves measuring the subject's motor skills. Twenty randomly selected sober subjects take the test and produce a mean score of 41.0 with a standard deviation of 3.7. At the 0.01 level of significance, test the claim that the true mean score for all sober subjects is equal to 35.0. Use the traditional method of testing hypotheses.

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 the mean lifetime of car engines of a particular type is greater than 220,000 miles. Sample data are summarized as $n = 23 , \bar { x } = 226,450$ miles, and $\mathrm { s } = 11,500$ miles. Use a significance level of $\alpha = 0.01$

Provide an appropriate response -Test the claim that for the population of female college students, the mean weight is given by $\mu = 132 \mathrm { lb }$ . Sample data are summarized as $\mathrm { n } = 20 , \overline { \mathrm { x } } = 137 \mathrm { lb }$ , and $\mathrm { s } = 14.2 \mathrm { lb }$ . Use a significance level of $\alpha = 0.1$

Express the null hypothesis and the alternative hypothesis in symbolic form. Use the correct symbol (µ, p, ?) for the indicated parameter. -Carter Motor Company claims that its new sedan, the Libra, will average better than 25 miles per gallon in the city. Use $\mu$ , the true average mileage of the Libra.

Formulate the indicated conclusion in nontechnical terms. Be sure to address the original claim. -The manufacturer of a refrigerator system for beer kegs produces refrigerators that are supposed to maintain a true mean temperature, µ, of 42°F, ideal for a certain type of German pilsner. The owner of the brewery does not agree with the refrigerator manufacturer, and claims he can prove that the true mean temperature is incorrect. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is to reject the null hypothesis, state the conclusion in nontechnical terms.

Formulate the indicated conclusion in nontechnical terms. Be sure to address the original claim. -A skeptical paranormal researcher claims that the proportion of Americans that have seen a UFO, p, is less than 2 in every ten thousand. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is failure to reject the null hypothesis, state the conclusion in nontechnical terms.

Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim. -According to a recent poll 53% of Americans would vote for the incumbent president. If a random sample of 100 people results in 45% who would vote for the incumbent, test the claim that the actual percentage is 53%. Use a 0.10 significance level.

The owner of a football team claims that the average attendance at games is over 63,500, and he is therefore justified in moving the team to a city with a larger stadium.

Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim -A supplier of digital memory cards claims that no more than 1% of the cards are defective. In a random sample of 600 memory cards, it is found that 3% are defective, but the supplier claims that this is only a sample fluctuation. At the 0.01 level of significance, test the supplier's claim that no more than 1% are defective.

Find the P-value for the indicated hypothesis test. -In a sample of 88 children selected randomly from one town, it is found that 8 of them suffer from asthma. Find the P-value for a test of the claim that the proportion of all children in the town who suffer from asthma is equal to 11%.

Find the P-value for the indicated hypothesis test. -Find the P-value for a test of the claim that less than 50% of the people following a particular diet will experience increased energy. Of 100 randomly selected subjects who followed the diet, 47 noticed an increase in their energy level.

An article in a journal reports that 34% of American fathers take no responsibility for child care. A researcher claims that the figure is higher for fathers in the town of Littleton. A random sample of 225 fathers from Littleton, yielded 97 who did not help with child care. Find the P-value for a test of the researcher's claim.

Find the P-value for the indicated hypothesis test. -A manufacturer claims that fewer than 6% of its fax machines are defective. In a random sample of 97 such fax machines, 5% are defective. Find the P-value for a test of the manufacturer's claim.

Provide an appropriate response -Kate asked her female friends whether they were vegetarian. Among 40 responses, 15 were responses of "yes". Is it valid to use these results to test the claim that the proportion of American women that are vegetarians is greater than 25%?