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Exam 8: Hypothesis Testing

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Question 31

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Express the null hypothesis and the altemative hypothesis in symbolic form. Use the correct symbol $( \mu , p , \sigma )$ for the indicated parameter. A psychologist claims that more than 5.8 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.

A) $\begin{array} { l } H _ { 0 } : p = 5.8 \% \\H _ { 1 } : p < 5.8 \%\end{array}$
B) $\begin{array} { l } H _ { 0 } : p = 5.8 \% \\H _ { 1 } : p \leq 5.8 \%\end{array}$
C) $\begin{array} { l } H _ { 0 } : p = 5.8 \% \\H _ { 1 } : p > 5.8 \%\end{array}$
D) $\begin{array} { l } H _ { 0 } : p < 5.8 \% \\H _ { 1 } : p \geq 5.8 \%\end{array}$

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Question 32

Multiple Choice

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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) . With $H _ { l }$ : p>0.554 , the test statistic is z=1.34 .

A) 0.9099 ; fail to reject the null hypothesis
B) 0.0901 ; reject the null hypothesis
C) 0.0901 ; fail to reject the null hypothesis
D) 0.1802 ; reject the null hypothesis

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Question 33

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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=0.52 .

Find the P -value for the indicated hypothesis test. 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 value of the test statistic z using $z = \frac { \hat { p } - p } { \sqrt { \frac { p q } { n } } }$ . The claim is that the proportion of drowning deaths of children attributable to beaches is more than 0.25 , and the sample statistics include n=696 drowning deaths of children with 30% of them attributable to beaches.

A chi-square hypothesis test is going to be conducted about a population standard deviation. Select the statement that is not true about the Chi-square test

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 4.7 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.

Express the original claim in symbolic form. Claim: 20% of adults smoke

A formal hypothesis test is to be conducted using the claim that the mean AC thermostat setting in restaurants is equal to $74 ^ { \circ } \mathrm { F }$ What is the null hypothesis and how is it denoted?

Find the P-value in a test of the claim that the mean IQ score of acupuncturists is equal to 100 , given that the test statistic is z=-2.00

A formal hypothesis test is to be conducted using the claim that the mean body temperature is equal to $98.6 ^ { \circ } \mathrm { F }$ What is the null hypothesis and how is it denoted?

Provide an appropriate response. Tim believes that a coin is coming up tails less than 50% of the time. He tests the claim p<0.5 . In 100 tosses, the coin comes up tails 57 times. What is the value of the sample proportion? Do you think the P -value will be small or large and what should Tim conclude about the claim p<0.5?

Find the value of the test statistic $z$ using $z = \frac { \hat { p } - p } { \sqrt { \frac { p q } { n } } }$ The claim is that the proportion of drowning deaths of children attributable to beaches is more than 0.25 , and the sample statistics include n=696 drowning deaths of children with 30 % of them attributable to beaches.

Which of the following is a requirement for testing a claim about a population proportion?

Use the traditional method to test the given hypothesis. Assume that the population is normally distributed and that the sample has been randomly selected. For randomly selected adults, IQ scores are nomally distributed with a standard deviation of 15. The scores of 14 randomly selected college students are listed below. Use a 0.10 significance level to test the claim that the standard deviation of IQ scores of college students is less than 15 . Round the sample standard deviation to three decimal places. $\begin{array} { l l l l l l l } 115 & 128 & 107 & 109 & 116 & 124 & 135 \\127 & 115 & 104 & 118 & 126 & 129 & 133\end{array}$

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 $\sigma$ 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.

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 cereal company claims that the mean weight of the cereal in its packets is 14 oz. The weights (in ounces)of the cereal in a random sample of 8 of its cereal packets are listed below. $\begin{array} { l l l l l l l l } 14.6 & 13.8 & 14.1 & 13.7 & 14.0 & 14.4 & 13.6 & 14.2\end{array}$ Test the claim at the 0.01 significance level.

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 32 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.

Solve the problem. 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.

Find the P -value in a test of the claim that the mean College Algebra final exam score of engineering majors equal to 88 , given that the test statistic is z=1.50 .