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

A candy manufacturer seeking to minimize the variation in weights of their candies claims to produce candies with a standard deviation less than $0.300$ g. Write the null and alternative hypotheses.

A survey claimed that $30\%$ of adults prefer electric cars over traditional cars. A car manufacturer believes the true proportion is higher than $30\%$. To test this, they survey a random sample of $50$ adults and find that $19$ 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.

$H_0:$ $p=0.4$

$H_a:$ $p\ne 0.4$

In a certain hypothesis test, $H_0:p=0.4$, $H_a:p$ < $0.4$. You collect a sample and calculate a test statistic $z=-1.32$. Find the $P$-value.

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.