Distributions Identify the distribution (normal, Student t , chi-square) that should be used in each of the following situations. If none of the three distributions can be used, what other method could be used?
a. In constructing a confidence interval of μ , you have 75 sample values and they appear to be from a population with a skewed distribution. The population standard deviation is not known.
b. In constructing a confidence
c. In constructing a confidence interval estimate of σ , you have 75 sample values and they appear to be from a population with a skewed distribution.
d. In constructing a confidence interval estimate of σ , you have 75 sample values and they appear to be from a population with a
e. In constructing a confidence interval estimate of p , you have 1200 survey respondents and 5% of them answered “yes” to the first question.
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- At a charter high school, the average GPA of a high school senior is known to be normally distributed. After a sample of 27 seniors is taken, the average GPA is found to be 2.85 and the sample variance is determined to be 0.16. Find a 95% confidence interval for the population mean GPA. a. 2.5615 to 2.8585 b. 2.6358 to 3.0642 c. 2.6917 to 3.0083 d. 2.5167 to 2.9033arrow_forwardYou would like to construct a 99% confidence interval to estimate today's population mean temperature, so you make a series of measurements (a random sample) throughout the day. The mean of these measurements is 58.5 degrees Fahrenheit, and their standard deviation is 3.0 degrees Fahrenheit. For each of the following sampling scenarios, determine which distribution should be used to calculate the critical value for the 99% confidence interval for the population mean.(In the table, Z refers to a standard normal distribution, and t refers to a t distribution.)arrow_forwardIf n=19, ¯x(x-bar)=34, and s=12, construct a confidence interval at a 95% confidence level. Assume the data came from a normally distributed population.Give your answers to one decimal place. ________________< μ <_____________________arrow_forward
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