Exam 10: B: Inference From Small Samples

Disinfectant Experiments Narrative An experiment to determine the efficacy of using 95% ethanol or 20% bleach as a disinfectant in removing bacterial and fungal contamination when culturing plant tissues was repeated 15 times for each disinfectant. The plant tissue being cultured was sweet potato: Five cuttings per plant were placed on a petri dish for each disinfectant and stored at 25°C for four weeks. The observation reported was the number of uncontaminated eggplant cuttings after the four-week storage. Disinfectant -Refer to Disinfectant Experiments Narrative. Is it reasonable to assume that the underlying variances are equal? Justify your conclusion.

Laptop Battery Charge Time Narrative A computer laboratory manager was in charge of purchasing new battery packs for her lab of laptop computers. She narrowed her choices to two models that were available for her machines. Since the models cost about the same, she was interested in determining whether there was a difference in the average time the battery packs would function before needing to be recharged. She took two independent random samples and computed the following summary information: -Set up the rejection regions for the following testing conditions. Assume the assumptions of normality and equal variances are satisfied. a. . = 10, = 12, and = 0.05. b. . = 4, = 8, and = 0.01. c. . = 15, = 15, and = 0.05.

Temperature Average Narrative The average low temperature for Victoria, B.C. in September is 12°C. The average low temperature for each of eight randomly selected years is 11.0, 12.4, 11.8, 10.9, 11.4, 12.2, 10.8, and 12.2. Assume the September low temperature distribution is normal. Do the sample data suggest the average low temperature is lower than 12°C? -Refer to Temperature Average Narrative. Compute the approximate p-value associated with the test statistic in the previous question. Do the sample data support the null hypothesis at the $\alpha$ = 0.1 level? Justify your conclusion.

Children Narrative Two random samples of 3-year-old children, each of size 25, are taken from independent populations. The populations are distributed with equal variances. The first sample has a mean of 35.5 and a standard deviation of 3.0 while the second sample has a mean 33.0 and standard deviation of 4.0. A test for the difference between the two population means is conducted on this data. -Refer to Children Narrative. How many degrees of freedom does this test have?