Homework 08

39. A doctor uses a new diagnostic test to indicate whether a patient has a certain disease. The doctor will prescribe medication for the patient if the doctor believes the patient has the disease, as indicated by the diagnostic test. The situation is similar to using a null hypothesis and an alternative hypothesis to decide whether to prescribe the medication. The hypotheses can be stated as follows. Ho :The patient does not have the disease. Ha :The patient has the disease. Which of the following best describes the power of the test? (A) The probability that the new test is better than an older test to indicate whether a patient has the disease (B) The probability that the new test indicates the disease in a patient who has the disease (C) The probability that the new test indicates the disease in a patient who does not have the disease (D) The probability that the new test does not indicate the disease in a patient who has the disease (E) The probability that the new test does not indicate the disease in a patient who does not have the disease

(B) The probability that the new test indicates the disease in a patient who has the disease

For which of the following pairs of significance levels and p-values are the results statistically significant? That is, for each α, should H0 be rejected based on the given p-value? Select all cases where H0 should be rejected:

- significance level = 0.100; p-value=0.003 - significance level = 0.050; p-value=0.008

In a study of a weight loss program, 2 subjects lost an average of 10 lbs after 5 weeks. Methods of statistics can be used to show that it is likely to get these results by chance if the diet had no​ effect. 1. Does the weight loss program have statistical​ significance? 2. Does the weight loss program have practical​ significance?

1. No 2. Yes

You are conducting a study to see if the probability of catching the flu this year is significantly less than 0.2. You use a significance level of α=0.05. H0:p=0.2 H1:p<0.2 You obtain a sample of size n=602 in which there are 99 successes. 1. What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic = 2. What is the p-value for this sample? (Report answer accurate to four decimal places.) p-value = 3. The p-value is... 4. This test statistic leads to a decision to... 5. As such, the final conclusion is that...

1. test statistic = -2.180 2. p-value = 0.0146 3. less than (or equal to) significant level 4. reject the null 5. The sample data support the claim that the probability of catching the flu this year is less than 0.2.

Which of the following statements about P-value is correct?

An extremely small P-value indicates that the actual data is very different from that expected if the null hypothesis is true.

Type II error is:

Failing to reject a false null hypothesis

You are conducting a study to see if the proportion of voters who prefer Candidate A is significantly more than 0.34. Thus you are performing a right-tailed test. Your sample data produce the test statistic z=2.74. Find the P-value accurate to 4 decimal places. P- value =

P- value = 0.0031

A hypothesis test produced a p-value of 0.0764. If the test was conducted at the significance level αα=0.1, which of the following is correct about the result?

Reject H0; a Type I error is possible.

Type I error is:

Rejecting a true null hypothesis

When testing a new treatment, what is the difference between statistical significance and practical significance? Can a treatment have statistical significance, but not practical significance?

Statistical significance is achieved when the result is very unlikely to occur by chance. Practical significance is related to whether common sense suggests that the treatment makes enough of a difference to justify its use. It is possible for a treatment to have statistical significance, but not practical significance.

When we report that something is statistically significant from a significance test, it means that which of the following is TRUE?

The findings are unlikely to occur if the null hypothesis is true.

The trustees of a local school district commission a survey to determine voter opinions about a possible bond measure to fund school upgrades. In a poll of 293 of the district's 5,019 registered voters, 178 would support the bond measure. A hypothesis test was conducted using StatCrunch to determine if such a bond would pass with the required 55% of the vote. Which of the following interpretations of the p-value as a probability statement for the scenario is NOT CORRECT?

The p-value is the probability of that a randomly sampled person in this data set supported the bond measure, assuming the null hypothesis is true.

For a certain statistical test (conducted at a 10% significance level), the power of the test was determined to be 0.79. Determine the following. (Enter your answer as a decimal.) a (the probability of a Type I error) is B (the probability of a Type II error) is

Type I error = 0.10 Type II error = 0.21

Suppose the P-value for testing hypotheses was computed to be 0.057. Which of the following statements is correct?

We can reject the null hypothesis at the significance level alpha = 0.10 but not at 0.05 or 0.01

4.44 Nearsighted: It is believed that nearsightedness affects about 8% of all children. In a random sample of 194 children, 21 are nearsighted. Conduct a hypothesis test using the 5% significance level. a) Construct hypotheses appropriate for the following question: Do these data provide evidence that the 8% value is inaccurate? b) What proportion of children in this sample are nearsighted? Round your answer to 4 decimal places. c) Given that the standard error of the sample proportion is 0.0195 and the point estimate follows a nearly normal distribution, calculate the test statistic (use the z-statistic). Round your answer to 2 decimal places. d) What is the p-value for this hypothesis test? Round your answer to 4 decimal places. e) What is the decision for this hypothesis test?

a) H : p = 0.08 H : p not= 0.08 b) 0.1082 c) 1.45 z = p^-p/SE d) 0.1471 p = 2*(1 - P(Z<1.45)) e) Since p ≥ α we do not have enough evidence to reject the null hypothesis, so we fail to reject the null hypothesis

According to areport on consumer fraud and identity theft, 21% of all complaints during one year were for identity theft. In that year, Louisiana had 323 complaints of identity theft out of 1491 consumer complaints. Does this data provide enough evidence to show that Louisiana had a lower proportion of identity theft than 21%? State the Type I and Type II errors in this case. a) State the Type I error. b) State the Type II error.

a) Concluding that the proportion of complaints from identity theft in Louisiana is less than 21%, when it is 21%. b) Concluding that the proportion of complaints from identity theft in Louisiana is 21%, when it is less than 21%.

The US Department of Energy reported that 45% of homes were heated by natural gas. A random sample of 350 homes in Oregon found that 177 were heated by natural gas. Test the claim that proportion of homes in Oregon that were heated by natural gas is different than what was reported. Use a 1% significance level. Give answer to at least 4 decimal places. a. What are the correct hypotheses? (Select the correct symbols and use decimal values not percentages.) H0 = H1 = Based on the hypotheses, compute the following: b. Test Statistic = c. p-value = d. Based on the above we choose to e. The correct summary would be: _______________ that the proportion of homes in Oregon that were heated by natural gas is different than what the DOE reported value of 45%.

a. H0 : p = 0.45 H1 : p not= 0.45 b. ? c. ? d. Fail to reject the null hypothesis e. There is not enough evidence to support the claim

A sociologist claims the probability that a person picked at random in Times Square in New York City is visiting the area is 0.83. You want to test to see if the proportion is actually lower. a. Identify the null and alternative hypotheses. H0 = HA = b. Identify the type I error. c. Identify the type II error.

a. H0 : p = 0.83 HA : p < 0.83 b. You decide that the proportion of people in Times Square who are visiting is NOT 0.83, when, in reality, the proportion of people in Times Square who are visiting is 0.83. c. You decide that the proportion of people in Times Square who are visiting is 0.83, when, in reality, the proportion of people in Times Square who are visiting is NOT 0.83.

a. H0 is true ; We reject the H0 = b. H0 is true ; We fail to reject H0 = c. H0 is false ; We reject the H0 = d. H0 is false ; We fail to reject H0 =

a. Type 1 Error b. Correct Decision c. Correct Decision d. Type 2 Error

The significance level alpha, α, is most directly associated with...

making a Type I error

Suppose we are testing the hypotheses H0: p=0.3 vs. Ha: p>0.3. Of the following sample proportions, which one will have the smallest P-value? (Hint: Draw a sampling distribution of sample proportion centered at the value under H0 and mark these different values of p^ to compare their tail probabilities in the direction of on Ha.)

p^ = 0.5