BackForecast and Actual Temperatures Listed below are actual temperatures (°F) along with the temperatures that were forecast five days earlier (data collected by the author). Use a 0.05 significance level to test the claim that differences between actual temperatures and temperatures forecast five days earlier are from a population with a mean of 0°F.
Questions 6–10 refer to the sample data in the following table, which describes the fate of the passengers and crew aboard the Titanic when it sank on April 15, 1912. Assume that the data are a sample from a large population and we want to use a 0.05 significance level to test the claim that surviving is independent of whether the person is a man, woman, boy, or girl.
Given that the P-value for the hypothesis test is 0.000 when rounded to three decimal places, what do you conclude? What do the results indicate about the rule that women and children should be the first to be saved?
Claim of “At Least” or “At Most”
How do the following results change?
a. Chapter Problem claim is changed to this: “At least 50% of Internet users utilize two-factor authentication to protect their online data.”
Test Statistics
In Exercises 9–12, refer to the exercise identified and find the value of the test statistic. (Refer to Table 8-2 to select the correct expression for evaluating the test statistic.)
Exercise 5 “Landline Phones”
A popular theme park claims that their weekly attendance is around . You believe that the weekly attendance is different than this claimed value, so you gather sample data. Write the null and alternative hypotheses.
A candy manufacturer seeking to minimize the variation in weights of their candies claims to produce candies with a standard deviation less than g. Write the null and alternative hypotheses.
A survey claimed that of adults prefer electric cars over traditional cars. A car manufacturer believes the true proportion is higher than . To test this, they survey a random sample of adults and find that say they prefer electric cars. Determine which test statistic to use & calculate it.
Determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed.
In a certain hypothesis test, , < . You collect a sample and calculate a test statistic . Find the -value.
Stem Cell Survey In a Newsweek poll of 882 adults, 481 (or 55%) said that they were in favor of using federal tax money to fund medical research using stem cells obtained from human embryos. A politician claims that people don’t really understand the stem cell issue and their responses to such questions are random responses equivalent to a coin toss. Use the following probabilities related to determining whether the result of 481 is significantly high (assuming the true rate is 50%). Is 481 significantly high? What should be concluded about the politician’s claim? Explain.
P(respondent says to use the federal tax money) = 0.5
P(among 882, exactly 481 says to use federal tax money) = 0.000713
P(among 882,481 or more say to use federal tax money) = 0.00389
Final Conclusions
In Exercises 21–24, use a significance level of α = 0.05 and use the given information for the following:
State a conclusion about the null hypothesis. (Reject H0 or fail to reject H0.)
Without using technical terms or symbols, state a final conclusion that addresses the original claim
Original claim: More than 35% of air travelers would choose another airline to have access to inflight Wi-Fi. The hypothesis test results in a P-value of 0.00001.
Final Conclusions
In Exercises 21–24, use a significance level of α = 0.05 and use the given information for the following:
State a conclusion about the null hypothesis. (Reject H0 or fail to reject H0.)
Without using technical terms or symbols, state a final conclusion that addresses the original claim.
Original claim: The mean pulse rate (in beats per minute) of adult males is 72 bpm. The hypothesis test results in a P-value of 0.0095.
Type I and Type II Errors
In Exercises 25–28, provide statements that identify the type I error and the type II error that correspond to the given claim. (Although conclusions are usually expressed in verbal form, the answers here can be expressed with statements that include symbolic expressions such as p = 0.1.)
The proportion of people who write with their left hand is equal to 0.1.
Type I and Type II Errors
In Exercises 25–28, provide statements that identify the type I error and the type II error that correspond to the given claim. (Although conclusions are usually expressed in verbal form, the answers here can be expressed with statements that include symbolic expressions such as p = 0.1.)
The proportion of drivers who make angry gestures is greater than 0.25.
Interpreting Power Chantix (varenicline) tablets are used as an aid to help people stop smoking. In a clinical trial, 129 subjects were treated with Chantix twice a day for 12 weeks, and 16 subjects experienced abdominal pain (based on data from Pfizer, Inc.). If someone claims that more than 8% of Chantix users experience abdominal pain, that claim is supported with a hypothesis test conducted with a 0.05 significance level. Using 0.18 as an alternative value of p, the power of the test is 0.96. Interpret this value of the power of the test.