A psychologist wants to test whether there is any difference in puzzle-solving abilities between boys and girls. Independent samples of twelve boys and fourteen girls were chosen at random. The boys took a mean of 37 minutes to solve a certain puzzle, with a standard deviation of 4.3 minutes. The girls took a mean of 32 minutes to solve the same puzzle, with a standard deviation of 5.4 minutes. Assume that the two populations of completion times are normally distributed, and that the population variances are equal. Can we conclude, at the 0.05 level of significance, that the mean puzzle-solving times for boys, u, differs from the mean puzzle-solving times for girls, µz? Perform a two-tailed test. Then fill in the table below. Carry your intermediate computations to at least three decimal places and round your answers as specified in the table. (If necessary, consult a list of formulas.)

A sample of seven laptop computers had a variance of 25.88 years when the lifespan of the computer was studied.  Find the 90% confidence interval for the true variance of the lifespan of laptop computers.  Show all work leading up to your answer below

Researchers conducted an experiment to test the effects of alcohol. Errors were recorded in a test of visual and motor skills for a treatment group of 28 people who drank ethanol and another group of 28 people given a placebo. The errors for the treatment group have a standard deviation of 2.20, and the errors for the placebo group have a standard deviation of 0.77. Assume that the two populations are normally distributed. Use a 0.05 significance level to test the claim that both groups have the same amount of variation among the errors. Let sample 1 be the sample with the larger sample variance, and let sample 2 be the sample with the smaller sample variance. What are the null and alternative hypotheses? OB. Ho: 0=02 O A. H₁: 0²12 = 0²/2 H₁:0² > 0²/2 H₁:0² <0² O C. Ho: 0²/02/ H₁:0² = 0² Identify the test statistic. (Round to two decimal places as needed.) Use technology to identify the P-value. (Round to three decimal places as needed.) What is the conclusion for this hypothesis test?…

Insurance Company A claims that its customers pay less for car insurance, on average, than customers of its competitor, Company B. You wonder if this is true, so you decide to compare the average monthly costs of similar insurance policies from the two companies. For a random sample of 13 people who buy insurance from Company A, the mean cost is $150 per month with a standard deviation of $19. For 9 randomly selected customers of Company B, you find that they pay a mean of $157 per month with a standard deviation of $16. Assume that both populations are approximately normal and that the population variances are equal to test Company A's claim at the 0.05 level of significance. Let customers of Company A be Population 1 and let customers of Company B be Population 2. Step 2 of 3: Compute the value of the test statistic. Round your answer to three decimal places.

Research has shown that, for baseball players, good hip range of motion results in improved performance and decreased body stress. A research article reported on a study of independent samples of 40 professional pitchers and 40 professional position players. For the pitchers, the sample mean hip range of motion was 75.8 degrees and the sample standard deviation was 5.6 degrees, whereas the sample mean and sample standard deviation for position players were 79.9 degrees and 7.2 degrees, respectively. Assuming that the two samples are representative of professional baseball pitchers and position players, test hypotheses appropriate for determining if there is convincing evidence that the mean range of motion for pitchers is less than the mean for position players. (Use  ? = 0.05.  Use ?1 for pitchers and ?2 for position players.)

The adult eastern hellbender (a type of giant salamander) has a length which is normally distributed with a mean of 31.8 cm and a standard deviation of 2.7 cm, while the adult Ozark hellbender has a length which is normally distributed with a mean of 34.9 and a standard deviation of 4.5. Random samples of a size 100 are selected of each species of hellbender. The box plots are created for each dataset. Which box plot will most likely have the larger interquartile range? O a. The IQR will be around the same for each. 0. O b. Either is equally likely to be larger than the other. 0 O c. The Ozark hellbenders. 0 O d. The eastern hellbenders. 0

A custodian wishes to compare two competing floor waxes to decide which one is best. He believes that the mean of WaxWin is greater than the mean of WaxCo. In a random sample of 40 floors of WaxWin and 43 of WaxCo. WaxWin had a mean lifetime of 26.3 and WaxCo had a mean lifetime of 28. The population standard deviation for WaxWin is assumed to be 7.1 and the population standard deviation for WaxCo is assumed to be 6.1. Perform a hypothesis test using a significance level of 0.05 to help him decide. Let WaxWin be sample 1 and WaxCo be sample 2. The correct hypotheses are: O Ho: µ1 H2(claim) Ο H: μι μp HA: H1 < µ2(claim) O Ho: µ1 = 2 HA: μι μ (claim) Since the level of significance is 0.05 the critical value is 1.645 The test statistic is: (round to 3 places) The p-value is: (round to 3 places) The decision can be made to: O reject Ho O do not reject Ho The final conclusion is that: O There is enough evidence to reject the claim that the mean of WaxWin is greater than the mean of WaxCo.…

Research has shown that, for baseball players, good hip range of motion results in improved performance and decreased body stress. A research article reported on a study of independent samples of 40 professional pitchers and 40 professional position players. For the pitchers, the sample mean hip range of motion was 75.5 degrees and the sample standard deviation was 5.8 degrees, whereas the sample mean and sample standard deviation for position players were 79.1 degrees and 7.1 degrees, respectively. Assuming that the two samples are representative of professional baseball pitchers and position players, test hypotheses appropriate for determining if there is convincing evidence that the mean range of motion for pitchers is less than the mean for position players. (Use  ? = 0.05.  Use ?1 for pitchers and ?2 for position players.) State the appropriate null and alternative hypotheses.   Find the test statistic and P-value. (Use SALT. Round your test statistic to one decimal place and…

According to the College Board, scores on the math section of the SAT Reasoning college entrance test for the class of 2010 had a mean of 516 and a standard deviation of 116. Assume that they are roughly normal.One of the quartiles of the scores from the math section of the SAT Reasoning test is 438. The other quartile is _______.

Steve believes that his wife's cell phone battery does not last as long as his cell phone battery. On eleven different occasions, he measured the length of time his cell phone battery lasted and calculated that the mean was 16.4 hours with a standard deviation of 6.4 hours. He measured the length of time his wife's cell phone battery lasted on seven different occasions and calculated a mean of 23.3 hours with a standard deviation of 4.2 hours. Assume that the population variances are the same. Let Population 1 be the battery life of Steve's cell phone and Population 2 be the battery life of his wife's cell phone. Step 1 of 2: Construct a 90 % confidence interval for the true difference in mean battery life between Steve's cell phone and his wife's. Round the endpoints of the interval to one decimal place, if necessary.