Exam 8: Hypothesis Testing

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 2.4 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.

Use the traditional method to test the given hypothesis. Assume that the population is normally distributed and that the sample has been randomly selected. -With individual lines at the checkouts, a store manager finds that the standard deviation for the waiting times on Monday mornings is 5.2 minutes. After switching to a single waiting line, he finds that for a random sample of 29 customers, the waiting times have a standard deviation of 4.8 minutes. Use a 0.025 significance level to test the claim that with a single line, waiting times vary less than with individual lines.

Determine whether the given conditions justify testing a claim about a population mean µ -A hypothesis test is performed to test the claim that a population proportion is greater than $0.7$ . Find the orobability of a type II error, $\beta$ , given that the true value of the population proportion is $0.72$ . The sample size is 50 and the significance level is 0,05 .

A researcher claims that 62% of voters favor gun control. 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.

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 public bus company official claims that the mean waiting time for bus number 14 during peak hours is less than 10 minutes. Karen took bus number 14 during peak hours on 18 different occasions. Her mean waiting time was 7 minutes with a standard deviation of 2.3 minutes. At the 0.01 significance level, test the claim that the mean is less than 10 minutes.

Use the traditional method to test the given hypothesis. Assume that the population is normally distributed and that the sample has been randomly selected. -At the $\alpha = 0.05$ significance level test the claim that a population has a standard deviation of $20.3$ . A random sample of 18 people yields a standard deviation of $27.1$ .

Provide an appropriate response. -List three phrases which are associated with one-tailed claims.

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 cereal company claims that the mean weight of the cereal in its packets is at least $14 \mathrm { oz }$ .

Determine whether the hypothesis test involves a sampling distribution of means that is a normal distribution, Student t distribution, or neither. -Claim: $\mu = 119$ . Sample data: $n = 15 , \bar { x } = 103 , s = 15.2$ . The sample data appear to come from a normally distributed population with unknown $\mu$ and $\sigma$ .

Use the traditional method to test the given hypothesis. Assume that the population is normally distributed and that the sample has been randomly selected. -In one town, monthly incomes for men with college degrees are found to have a standard deviation of $650. Use a 0.01 significance level to test the claim that for men without college degrees in that town, incomes have a higher standard deviation. A random sample of 22 men without college degrees resulted in incomes with a standard deviation of $901.