The null hypothesis is what we intend to either reject or fail to reject using our sample data. In this case, the null hypothesis is that Josh cannot shoot more than 50 points on average, and Josh's performance in 10 games are the sample data we use to assess this hypothesis. 

The null hypothesis is the default hypothesis and predicts that there is no relationship between the variables in question.  Each of the incorrect answer choices here either predicts a relationship between variables or makes a broad assertion that includes much more than the variables in question.

The statistician has determined that she will only reject the null hypothesis if she has 95% confidence that there is a relationship between variables. 

To have this level of confidence, the statistician must obtain a p value of 0.05 or lower.

Therefore, she should not reject the null hypothesis since 0.1 is greater that 0.05.

The hypotheses tested here are: 

 The true mean pollution level is within the allowed limit.

 The true mean pollution level is higher than the allowed limit. 

The type I error occurs when the null hypothesis is rejected even though it is actually true. In this case, the type I error would be deciding that the mean pollution levels are higher than the allowed limit and closing the drinking water pipelines. 

Because we are comparing one sample to a known mean, the hypothesis is  compared to the known average, 23.  We would like to test the claim that meditating will increase focus time, therefore our null hypothesis must include all other outcomes. Therefore, the null is that Mu is less than or equal to 23. 

This question is about a linear regression between time spent meditating and time spent studying. Therefore, the hypothesis is regarding Beta1, the slope of the line. We are testing a non-directional or bi-directional claim that the relationship is significant. Therefore, the null hypothesis is that the relationship is not significant, meaning the slope of the line is equal to zero.

Because we are comparing more than 2 groups, we must use an ANOVA for this problem. For an ANOVA problem, the null hypothesis is that all of the groups’ means are the same.

Because the same students are tested twice, this is a paired study, therefore we must use a hypothesis appropriate for a paired t-test.  The hypothesis for a paired t-test regards the average of the differences between before and after treatment, called MuD. We are testing the claim that vitamins increase study time, which would mean that study time for vitamin users would be greater than that of the control.  Therefore the null must include all other outcomes. The null hypothesis should state that the difference between before and after treatment is greater than or equal to zero.

Susy wants to know whether ants in her neighborhood have smaller colonies, so that will be her alternative hypothesis. Therefore her null hypothesis needs to cover all other outcomes, that the colony sizes are greater than or equal to average colony size of 4000 ants.

Timmy does not have a directional hypothesis, he only wants to know whether local ant colonies are different from average. Therefore he thinks the colonies could be bigger or smaller than average. This means his alternative hypothesis is that the ant colonies are NOT equal to the average colony size of 4000 ants. His null hypothesis must include all other outcomes, which in this case is that local ant colonies are equal to the average size of 4000 ants.