Exam 11: Inference for a Normal Population

Consider the figure shown indicating the number of moles on the skin of a set of 25 patients examined by a dermatologist. Published reports claim that the mean number for the population these patients come from is 3.5 moles. Conduct a one-sample t-test on this data and determine whether this seems to be true. Assume a = 0.5. In your answer present the following: your calculated t-value, an exact P-value using a computer or a range for the P-value using a table of critical values, and a statement about whether the population mean appears to be 3.5 or not based on the sample. ​

Consider a situation in which Jamal measures the resting heart rate of 16 individuals from a population that he thinks (based on published reports) has an average resting heart rate of 72 beats per minute. His sample has a mean of 75.2 with a standard deviation of 6.2 cm. Based on his t-test statistic, and using your table of critical t-values, which of the following P-value ranges matches the one for the t-value he obtains?

Using your table of critical t-values, what values of t correspond to the ones that bound a central region containing 90% of the distribution when there are 16 degrees of freedom?

For the data set shown below, calculate the following values: sample mean, 95% confidence interval for the population mean, sample variance, 95% confidence interval for the population variance, sample standard deviation, approximate 95% confidence interval for the population standard deviation. Data: 2 2 3 3 3 4 4 4 4 4 5 5 5 5 5 5 5 6 6 6 6 6 7 7 7 8 8

If a sample with 34 values has a mean of 33 and a standard deviation of 35, how many degrees of freedom does it have?

For a pair of samples with the same standard deviation, but where the second has a sample size twice as large, the 95% confidence interval for the second sample is half as wide as the first.

If we have a 95% confidence interval of 14.69 < μ < 15.85 based on a sample of 18 values, what is the standard deviation of the sample?

If we have a sample of 14 values that gives us a 99% confidence interval of 5.76 < μ < 8.54, what is the standard deviation of the sample?

Consider a data sample consisting of 12 values with a mean of 22 and standard deviation of 1.5. What is the approximate 95% confidence interval for the standard deviation?

What is the correct representation for the 5% critical t-value for a sample with 9 degrees of freedom?

For the data set shown below, calculate the following values: sample mean, 95% confidence interval for the population mean, sample variance, 95% confidence interval for the population variance, sample standard deviation, approximate 95% confidence interval for the population standard deviation. Data: 1 2 2 2 3 3 3 3 4 4 4 4 4 4 5 5 5 5 6 6 6 7

Consider a data sample consisting of 12 values with a mean of 22 and variance of 1.5. What is the 95% confidence interval for the variance?

If a t-test results in a sample mean the same as the hypothesized population mean, then the t-statistic and P-value of the test would be which of the following (respectively)?

The t-distribution is wider than the normal distribution.

Consider a data sample consisting of 12 values with a mean of 22 and standard deviation of 1.5. What is the 95% confidence interval for the variance?

How many standard errors in width is the 95% confidence interval for a sample with 20 values?

Consider the figure shown indicating the number of moles on the skin of a set of 30 patients examined by a dermatologist. Published reports claim that the mean number for the population these patients come from is 3.4 moles. Conduct a one-sample t-test on this data and determine whether this seems to be true. Assume a = 0.5. In your answer, present the following: your calculated t-value, an exact P-value using a computer or a range for the P-value using a table of critical values, and a statement about whether the population mean appears to be 3.4 or not based on the sample. ​ ​

The t-distribution is wider for larger sample sizes than for smaller ones.

For a t-test using a sample of 35 values which returns a positive value, how big must the t-test statistic be to reject the null hypothesis?

Consider an experiment in which Shireen measures 20 Arabidopsis plants in a pasture that an agricultural company claims have an average height of exactly 23 cm. Her plants have a mean of 24.53 cm with a standard deviation of 2.33 cm, however. Based on her t-test statistic, and using your table of critical t values, which of the following P-value ranges matches the one for the t-value she obtains?