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The type of diet that promotes beneficial gut microbes is a

Please note that this question consists of six parts. Show all your work/explanation. Just giving the answer without adequate work/explanation may result in zero for the question.  The battery lifetime of particular type of calculator is supposed to last for 25,000 calculations on average.  A researcher suspects that these batteries are not as good as advertised. For a random sample of 16 batteries for such calculator type, the sample mean was found to be 24,680 calculations and standard deviation 482 calculations. Set up the appropriate null and alternative hypotheses for testing the question posed by the researcher. Are the conditions needed to carry out the test in part 1 satisfied? In addition to answering yes or no, clearly state the conditions and explain how you check.   Find the test statistic for the test in part 1. Show your calculations. Find the rejection region for the test in part 1 using 5% significance level. Clearly state the rejection region (it is not sufficient to provide just the critical value). Write the final conclusion in the context of the problem. Based on the decision you made in part 5, which error: type I or type II is possible? Explain.   

Suppose for the test of   Vs    the p-value is 0.018. If the true population proportion is 0.45, then the probability of observing a test statistic as extreme or even more extreme than the one actually observed is 0.018. Is this statement true or false?

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For hypothesis tests or confidence intervals for a mean, the Central Limit Theorem allows the researcher to assume that the sample comes from a normal population, as long as the sample size is large. Is this statement true or false?

For each of the statements below, state if it is true or false.  T distribution is symmetric around 0. This is a [fill1] statement. If random variable T has t distribution with 10 degrees of freedom, then

After being diagnosed with a bacterial infection, an oral (taken by mouth) antibiotic was prescribed. After taking the full course of the antibiotic, what would be an expected outcome of the gut microbiome?   ​

Species richness describes

Which type of eukaryotic organism evolved first?

Biodiversity is best defined as