Perform a Two Sample Hypothesis Test for Means and perform a Two Sample Hypothesis Test for Proportions. For the Hypothesis Tests, make sure to report the following steps:
1. Identify the null hypothesis, Ho, and the alternative hypothesis, Ha.
2. Determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed.
3. Find the critical value(s) and identify the rejection region(s).
4. Find the appropriate standardized test statistic. If convenient, use technology.
5. Decide whether to reject or fail to reject the null hypothesis.
6. Interpret the decision in the context of the original claim
A science teacher claims that the mean scores on a science assessment test for fourth grade boys and girls are equal. The mean score for 53 randomly selected boys is 138 with a standard deviation of 39, and the mean score for 75 randomly selected girls is 138 with a standard deviation of 30. At α = 0.05, can you reject the teacher's claim? Assume the populations are normally distributed and the population variances are equal. In a random sample of 1022 U.S. adults, 480 think that the U.S. government is doing too little to protect the environment. In another random sample of 1008 U.S. adults taken 10 years ago, 514 think that the U.S. government is doing too little to protect the environment. At α = 0.10, can you reject the claim that the proportion of U.S. adults who think that the U.S. government is doing too little to protect the environment is less than it was 10 years ago?