Researchers studying the effects of diet on growth would like to know if a vegetarian diet affects the height of a child. The researchers randomly selected 12 vegetarian children that are six years old. The average height of the children is 42.5 inches with a standard deviation of 3.8 inches. The average height for all six year old children is 45.75 inches. Conduct a hypothesis test to determine whether there is overwhelming evidence at a = 0.05 that six year old vegetarian children are not the same height as other six year old children. Assume that the heights of six year old vegetarian children are approximately normally distributed.

A college lacrosse coach wants to know if sending his players to a training camp will help them to score more goals.  He knows that the population mean scoring per game for all college teams is 12.4 per game, with a standard deviation of 2.48.  He takes a sample of 36 teams that have been to this training camp and he finds that they averaged 13.3 goals per game. Will participating in this training camp help his team score more goals? Use alpha .05 to answer this question.

A study was conducted for an aviation safety agency in which they surveyed thousands of passengers at airports across Europe. In this study, the "mass" for a passenger includes the weight of the passenger and all of the passenger's carry-on items, including infants without their own seats. For the 5,904 adult male passengers measured in summer, the sample mean and standard deviation for this mass were 88.8 kg and 15.9 kg, respectively.   (a) Construct a 95% confidence interval (in kilograms) for the population mean mass for adult male passengers in summer. (Round your answers to three decimal places.) ___to__ kg (b) Write a sentence or two interpreting the confidence interval you found in part (a). With 95% confidence, we can estimate that the population mean mass of male passengers traveling in the summer is contained within the interval. We can estimate that 95% of the male passengers traveling in the summer in the sample have a mass that is contained within the interval.…

A Two-Sample Hypothesis TestThe mean number of English courses taken in a two-year time period by male and female college students is believed to be about the same. An experiment is conducted and data are collected from 29 males and 16 females. The males took an average of three English courses with a standard deviation of 0.8. The females took an average of four English courses with a standard deviation of 1.0. Are the means statistically the same? (Assume a 5% level of significance.)Useful tools:Normal Distribution Calculatort-Distribution Calculator 1. Which of the following null and alternative hypotheses match this scenario? A---H0:Δμ=0H0:Δμ=0Ha:Δμ≠0Ha:Δμ≠0 B---H0:Δμ≠0H0:Δμ≠0Ha:Δμ=0Ha:Δμ=0 C---H0:Δμ=0H0:Δμ=0Ha:Δμ>0 2. Which type of test should be applied? A---The alternative hypothesis indicates a right-tailed test. B---The alternative hypothesis indicates a left-tailed test. C---The alternative hypothesis indicates a two-tailed test. 3. Which type of distribution should be…

In a certain​ city, the average​ 20- to​ 29-year old man is 72.5 inches​ tall, with a standard deviation of 3.2 ​inches, while the average​ 20- to​ 29-year old woman is 64.3 inches​ tall, with a standard deviation of 3.9 inches. Who is relatively​ taller, a​ 75-inch man or a​ 70-inch woman?

Do political science classes require less writing than history classes? The 47 randomly selected political science classes assigned an average of 19 pages of essay writing for the course. The standard deviation for these 47 classes was 5.6 pages. The 56 randomly selected history classes assigned an average of 21.9 pages of essay writing for the course. The standard deviation for these 56 classes was 4.1 pages. What can be concluded at the a = 0.10 level of significance? For this study, we should use Select an answer a. The null and alternative hypotheses would be: Ho: Select an answer v Select an answer v Select an answer v H: Select an answer v Select an answer v Select an answer v b. The test statistic ? v = (please show your answer to 3 decimal places.) c. The p-value = (Please show your answer to 4 decimal places.) d. The p-value is ? va e. Based on this, we should Select an answer v the null hypothesis. f. Thus, the final conclusion is that ... O The results are statistically…

Dentists believe that a diet low in sugary foods can reduce the number of cavities in children. Ten children whose diets are believed to be high in sugar are examined and the mean number of cavities is 3.63.6 with a standard deviation of 1.31.3. Twenty children whose diets are believed to be low in sugar are examined and the mean number of cavities is 1.01.0 with a standard deviation of 0.30.3. Construct a 99%99% confidence interval for the true difference between the mean numbers of cavities for children whose diets are high in sugar and those whose diets are low in sugar. Assume that the variances of the two populations are the same. Let Population 1 be children whose diets are believed to be high in sugar and Population 2 be children whose diets are believed to be low in sugar. Round the endpoints of the interval to one decimal place, if necessary.