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The average height of females in the freshman class of a certain college has been 162.5 centimeters with a standard deviation of 6.9 centimeters. Is there reason to believe that there has been a change in the average height if a random sample of 50 females in the present freshman class has an average height of 165.2 centimeters? Use a P-value in your conclusion. Assume the standard deviation remains the same

It is claimed that an automobile is driven on the average more than 20,000 kilometers per year. To test this claim, a random sample of 100 automobile owners are asked to keep a record of the kilometers they travel. Would you agree with this claim if the random sample showed an average of 23,500 kilometers and a standard deyiation of 3900 kilometers? Use a P-value in your conclusion.

According to a dietary study, a high sodium intake may be related to ulcers, stomach cancer, and migraine headaches. The human requirement for salt is only 220 milligrams per day, which is surpassed in most single servings of ready- to-eat cereals. If a random sample of 20 similar servings of of certain cereal has a mean sodium content of 244 milligrams and a standard deviation of 24.5 milligrams, does this suggest at the 0.05 level of significance that the average sodium content for a single serving of such cereal is greater than 220 milligrams? Assume the distribution of sodium contents to be normal.

According to Chemical Engineering an important property of fiber is its water absorbency. The average percent absorbency of 25 randomly selected pieces of cotton fiber was found to be 20 with a standard deviation of 1.5 . A random sample of 25 pieces of acetate yielded an average percent of 12 with a standard deviation of \(125 .\) Is there strong evidence that the population mean percent absorbency for cotton fiber is significantly higher than the mean for acetate. Assume that the percent absorbency is approximately normally distributed and that the population variances in percent absorbency for the two fibers are the same. Use a significance level of 0.05

Past experience indicates that the time for high school seniors to complete a standardized test is a normal random variable with a mean of 35 minutes. If a random sample of 20 high school seniors took an average of 33.1 minutes to complete this test with a standard deviation of 4.3 minutes, test the hypothesis at the 0.05 level of significance that \(p=35\) minutes against the alternative that \(p<35\) minutes.

A manufacturer claims that the average tensile strength of thread A exceeds the average tensile strength of thread \(B\) by at least 12 kilograms. To test his claim, 50 pieces of each type of thread are tested under similar conditions. Type A thread had an average tensile strength of 86.7 kilograms with known standard deviation of \(\sigma A=6.28\) kilograms, while type B thread had an average tensile strength of 77.8 kilograms with known standard deviation of \(\sigma_{B}=5.61\) kilograms. Test the manufacturer's claim at \(\alpha=0.05 .\)

A study is made to see if increasing the substrate concentration has an appreciable effect on the velocity of a chemical reaction. With a substrate concentration of 1.5 moles per liter, the reaction was run 15 times with an average velocity of 7.5 micromoles per 30 minutes and a standard deviation of 1.5. With a substrate concentration of 2.0 moles per liter, 12 runs were made, yiclding an average velocity of 8.8 micromoles per 30 minutes and a sample standard deviation of 1.2 . Is there any reason to believe that this increase in substrate concentration causes an increase in the mean velocity by more than 0.5 micromole per 30 minutes? Use a 0.01 level of significance and assume the populations to be approximately normally distributed with equal variances.

A study was made to determine if the subject matter in a physics course is better understood when a lab constitutes part of the course. Students were randomly selected to participate in either a 3-semesterhour course without labs or a 4 -semester-hour course with labs. In the section with labs, 11 students made an average grade of 85 with a standard deviation of 4.7 and in the section without labs, 17 students made an average grade of 79 with a standard deviation of 6.1 . Would you say that the laboratory course increases the average grade by as much as 8 points? Use a P-value in your conclusion and assume the populations to be approximately normally distributed with equal variances.

10.35 To find out whether a new serum will arrest leukemia, 9 mice, all with an advanced stage of the disease, are selected. Five mice receive the treatment and 4 do not. Survival times, in years, from the time the experiment commenced are as follows. $$\begin{array}{l|ccccc}\text { Treatment } & 2.1 & 5.3 & 1.4 & 4.6 & 0.9 \\\\\hline \text { No Treatment } & 1.9 & 0.5 & 2.8 & 3.1 &\end{array}$$ At the 0.05 level of significance can the serum be said to be effective? Assume the two distributions to be normally distributed with equal variances.

10.36 \text { A large automobile manufacturing company is } trying to decide whether to purchase brand \(A\) or brand \(B\) tires for its new models. To help arrive at a decision, an experiment is conducted using 12 of each brand. The tires are run until they wear out. The results are $$\begin{aligned}\text { Brand } A: & x_{1}=37,900 \text { kilometers, } \\ & s_{1}=5,100 \text { kilometers. } \\\\\text { Brand B: } \quad x_{1} &=39,800 \text { kilometers, } \\\& s_{2}=5,900 \text { kilometers. }\end{aligned}$$ Test the hypothesis that there is no difference in the average wear of 2 brands of tires. Assume the populations to be approximately normally distributed with equal variances. Use a P-value.