Questions
1. For each of the following research questions:
1. State the Hypothesis
2. Explain why this is considered a one or two-tailed Hypothesis
3. State the Level of Significance
4. Calculate the test statistic
5. Calculate the P-value
6. State whether the Null Hypothesis is rejected (or not).
7. State your Conclusions.
8. State the assumptions that you were required to make to ensure that these conclusions were valid.
1.1 The objective of the experiment was to determine if common household mold can suppress or eliminate the growth of bacteria. To test this hypothesis, 24 Petri dishes were used, and a mixture of mold and bacteria was inoculated on each dish. The dishes were randomly distributed in a growth chamber and incubated for 48 hours. Then the bacterial count was determined. If the average bacterial count was less than 30 colonies per dish, the mold was considered to suppress bacterial growth. The sample mean bacterial count was 25 colonies per dish, and the sample standard deviation of the population distribution was known to be 2.1 colonies per dish. Test the hypothesis at the 2% level of significance.
1.2 A scientist is interested in understanding the effect of caffeine on the activity level of mice. The scientist randomly chose 15 mice, placed them in individual cages and provided a specified dose of caffeine to each of the mice. The activity level of the mice was recorded, and if there is a 15% change in the activity level over a week then the caffeine would be deemed to have an effect on the activity level of the mice. If the sample average % change in activity level was found to be 12.2%, and the change in activity level was known to have a standard deviation of 1.2%, test the hypothesis at the 7% level of significance.
1.3 How does increasing CO2 levels in the atmosphere affect the growth of Lodgepole pine seedlings? To investigate this, a scientist conducted an experiment where 80
seedlings were randomly assigned to individual growth chambers, and the seedlings were exposed to an atmosphere with a 3% increase in CO2 levels. After 6 months, the average change in the biomass of the seedlings was measured, and the sample mean was found to be 13.2 grams. It was also known that the population standard deviation for a 6-month-old pine seeding was 3.4 grams. Test to see if average change in seedling weight was greater than 15.2 grams at the 0.1% level of significance.
1.4 The human gut microbiome has been identified as a possible factor that affects the health of people. Often when people are prescribed antibiotics there is a change in the microbiome of the gut. An investigator was interested in determining the effect of a new antibiotic on the % change in the biome (keeping in mind that an antibiotic might increase or decrease the number of cells in the microbiome). Suppose 67 healthy individuals were chosen at random and prescribed a therapeutic level of the new antibiotic. If the sample mean of the % change in the gut microbiome was found to 4.2%, and known to have a population standard deviation of 0.3%, can this investigator conclude there is a change in the gut microbiome?
Questions
2. In a research study to help individuals who suffer from anorexia, an investigator randomly selected 29 individuals suffering from anorexia. The researcher then provided Cognitive-Behavior Therapy (CBT) to all 29 individuals to help them develop a healthier perception of body weight. At the conclusion of the therapy, the investigator calculated the weight gain for each of the 29 individuals (the differences are included in the table below (diff)). Using this data, and the known standard deviation of the population differences (6.8 Kg) answer the research question: Does Cognitive-Behavior Therapy help individuals increase their body weight? Please note that in the original dataset (provided), there was a single, large outlier. Please use plotting techniques to demonstrate how this outlier can be identified. Then replace that outlier with the correct value for the difference was -7.6 (note the outlier was found to be a transcription error in the original dataset so replacing the outlier with the correct value is the proper approach) and complete your investigation. Please use your statistical knowledge to answer the research question: Does CBT help anorexic patients gain weight?
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