Exam 8: Hypothesis Testing

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. -A large software company gives job applicants a test of programming ability and the mean for that test has been 160 in the past. Twenty-five job applicants are randomly selected from one large university and they produce a mean score and standard deviation of 183 and 12, respectively. Use a 0.05 level of significance to test the claim that this sample comes from a population with a mean score greater than 160.

Use the traditional method to test the given hypothesis. Assume that the population is normally distributed and that the sample has been randomly selected. -The standard deviation of math test scores at one high school is 16.1. A teacher claims that the standard deviation of the girls' test scores is smaller than 16.1. A random sample of 22 girls results in scores with a standard deviation of 14.3. Use a significance level of 0.01 to test the teacher's claim.

Determine whether the hypothesis test involves a sampling distribution of means that is a normal distribution, Student t distribution, or neither. -Claim: $\mu = 78$ . Sample data: $n = 24 , \bar { x } = 101 , s = 15.3$ . The sample data appear to come from a population with a distribution that is very far from normal, and $\sigma$ is unknown.

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. -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.

Express the null hypothesis $\mathrm { H } _ { 0 }$ and the alternative hypothesis $\mathrm { H } _ { 1 }$ in symbolic form. Use the correct symbol ( $\mu , \mathrm { p }$ , $\sigma$ )for the indicated parameter. -The owner of a football team claims that the average attendance at games is over 67,800, and he is therefore justified in moving the team to a city with a larger stadium.

Find the critical value or values of x $x ^ { 2 }$ based on the given information. - :\sigma>3.5 n=14 \alpha=0.05

Carter Motor Company claims that its new sedan, the Libra, will average better than 19 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.

Suppose that you are conducting a study on the effectiveness of a new teaching method and that you wish to use a hypothesis test to support your claim regarding the mean test score under this method. What restrictions are there in the wording of the claim? Will your claim become the null hypothesis or the alternative hypothesis, or does it depend on the situation? Give an example of a claim which is incorrectly worded.

Complete the following table on hypothesis testing. Test about Distribution Assumptions Mean Mean Proportion Variance

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. - $\alpha = 0.1$ for a two-tailed test.

Discuss the rationale for hypothesis testing. Refer to the comparison of the assumption and the sample results.

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 3.5" disks claims that no more than 1% of the disks are defective. In a random sample of 600 disks, 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. -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.

Express the null hypothesis $\mathrm { H } _ { 0 }$ and the alternative hypothesis $\mathrm { H } _ { 1 }$ in symbolic form. Use the correct symbol ( $\mu , \mathrm { p }$ , $\sigma$ )for the indicated parameter. -A skeptical paranormal researcher claims that the proportion of Americans that have seen a UFO, $p$ , is less than 2 in every one thousand.

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. -Use a significance level of $\alpha = 0.05$ to test the claim that $\mu \neq 32.6$ . The sample data consists of 15 scores for which $\bar { x } = 39.7$ and $s = 5$ .

Assume that a hypothesis test of the given claim will be conducted. Identify the type I or type II error for the test -A researcher claims that 62% of voters favor gun control. Identify the type II error for the test.

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: A roulette wheel is fair and in 40 consecutive spins of the wheel, black shows up 23 times. (A roulette wheel has 38 equally likely slots of which 18 are black).

Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim. -The health of employees is monitored by periodically weighing them in. A sample of 54 employees has a mean weight of 183.9 lb. Assuming that is known to be 121.2 lb, use a 0.10 significance level to test the claim that the population mean of all such employees weights is less than 200 lb.

Solve the problem. -A manufacturer finds that in a random sample of 100 of its CD players, 96% have no defects. The manufacturer wishes to make a claim about the percentage of nondefective CD players and is prepared to exaggerate. What is the highest rate of nondefective CD players that the manufacturer could claim under the following condition? His claim would not be rejected at the 0.05 significance level if this sample data were used. Assume that a left-tailed hypothesis test would be performed.

Assume that a hypothesis test of the given claim will be conducted. Identify the type I or type II error for the test -A cereal company claims that the mean weight of the cereal in its packets is at least 14 oz. Identify the type I error for the test.