Exam 8: Hypothesis Testing

Solve the problem. -For large numbers of degrees of freedom, the critical $\chi ^ { 2 }$ values can be approximated as follows: $\chi ^ { 2 } = \frac { 1 } { 2 } ( z + \sqrt { 2 k - 1 } ) ^ { 2 }$ where $\mathrm { k }$ is the number of degrees of freedom and $\mathrm { z }$ is the critical value. To find the lower critical value, the negat z-value is used, to find the upper critical value, the positive z-value is used. Use this approximation to estimate the critical value of $\chi ^ { 2 }$ in a right-tailed hypothesis test with $\mathrm { n } = 125$ and $\alpha = 0.01$ .

Use the given information to find the P-value -The test statistic in a right-tailed test is z = 1.43.

Provide an appropriate response. -Explain how to determine if a hypothesis test is one-tailed or two-tailed and explain how you know where to shade the critical region. Give an example for each which includes the claim, the hypotheses, and the diagram with the critical region shaded.

Solve the problem. -Write the claim that is suggested by the given statement, then write a conclusion about the claim. Do not use symbolic expressions or formal procedures: use common sense. A person claims to have extra sensory powers. A card is drawn at random from a deck of cards and without looking at the card, the person is asked to identify the suit of the card. He correctly identifies the suit 28 times out of 100.

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. - $\alpha = 0.08 ; H _ { 1 }$ is $\mu \neq 3.24$

Find the critical value or values of x $x ^ { 2 }$ based on the given information. - :\sigma<0.629 =19 \alpha=0.025

Solve the problem. -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 die is fair and in 100 rolls there are 63 sixes.

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 psychologist claims that more than 6.3 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.

Provide an appropriate response. -Suppose the claim is in the alternate hypothesis. What form does your conclusion take? Suppose the claim is in the null hypothesis. What form does your conclusion take?

In a hypothesis test, which of the following will cause a decrease in $\beta$ , the probability of making a type II error? A: Increasing $\alpha$ while keeping the sample size $n$ , fixed $B$ : Increasing the sample size $n$ , while keeping $\alpha$ fixed $\mathrm { C }$ : Decreasing $\alpha$ while keeping the sample size $n$ , fixed D: Decreasing the sample size $n$ , while keeping $\alpha$ fixed

In a hypothesis test, an increase in ? will cause a decrease in the power of the test provided the sample size is kept fixed.

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.

Assume that a hypothesis test of the given claim will be conducted. Identify the type I or type II error for the test -A skeptical paranormal researcher claims that the proportion of Americans that have seen a UFO, p, is less than 1 in every one thousand. Identify the type II error for the test.

Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim. -In a clinical study of an allergy drug, 108 of the 202 subjects reported experiencing significant relief from their symptoms. At the 0.01 significance level, test the claim that more than half of all those using the drug experience relief.

Find the critical value or values of x $x ^ { 2 }$ based on the given information. - :\sigma>26.1 =9 \alpha=0.01

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 researcher claims that $62 \%$ of voters favor gun control.

Determine whether the given conditions justify testing a claim about a population mean µ -The sample size is $\mathrm { n } = 39 , \sigma = 12.3$ , and the original population is not normally distributed.

Provide an appropriate response. -Define Type I and Type II errors. Give an example of a Type I error which would have serious consequences. Give an example of a Type II error which would have serious consequences. What should be done to minimize the consequences of a serious Type I error?

Use the traditional method to test the given hypothesis. Assume that the population is normally distributed and that the sample has been randomly selected. -Heights of men aged 25 to 34 have a standard deviation of $2.9$ . Use a $0.05$ significance level to test the claim that $t$ heights of women aged 25 to 34 have a different standard deviation. The heights (in inches) of 16 randomly selec women aged 25 to 34 are listed below. 62.13 65.09 64.18 66.72 63.09 61.15 67.50 64.65 63.80 64.21 60.17 68.28 66.49 62.10 65.73 64.72

Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim. -A poll of 1,068 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.