We use a t distribution for inference about a population mean instead of the standard Normal distribution:
if we do not know the population mean and must use the sample mean.
if the original population does not have a Normal distribution.
if we do not have a simple random sample.
if we do not know the population standard deviation and must use the sample standard deviation.
We use t distribution instead of Normal distribution, when population standard deviation is unknown and we use sample standard deviation.
Answer is option (d)
We use a t distribution for inference about a population mean instead of the standard Normal...
Solocting a distribution for inforences on the population mean Suppose that we want to estimate the number of holding penalties assessed during a college football game. The sample of games we pick has a mean of 3.4 penalties per game and a standard deviation of 0.7 penalties per game. For each of the following sampling scenarios, determine which test statistic is appropriate to use when making inference statements about the population mean. (In the table, Z refers to a variable...
For the following situations, tell what testing distribution you should use. (normal distribution, t-distribution, chi-square or ANOVA). a. A simple random sample of adults is obtained and the sample mean red blood cell count is measured. Assuming we know the population standard deviation, test the claim that the sample is from a population with a mean less than 5.4 cells/mL. b. A study of the flammability of children’s sleepwear across five different laboratories was done. Test the claim that the...
Determine if you are to use a normal distribution, a t-distribution, or a population proportion. Then, find the 95% confidence interval. a) In 34 randomly selected closing stock prices, the mean closing price was $19.96 and the population standard deviation was $2.62. Interval: b) In a random sample of 18 high school students, the mean hours spent on homework was 11.6 hours and the sample standard deviation was 3.04 hours. Interval: c) In a survey of 674 US males ages...
Suppose that we want to estimate the mean score on a nationwide examination in psychology, and for this purpose we choose a random sample of exam scores The sample we choose has a mean of 516 and a standard deviation of 75 . For each of the following sampling scenarios, determine which test statistic is appropriate to use when making inference statements about the population mean (In the table, Z refers to a variable having a standard normal distribution, and...
This Quiz: 22 pts possit Use the standard normal distribution or the t-distribution to construct a 99% confidence interval for the population mean. Justify your decision. If neither distribution can be used, explain why. Interpret the results. In a random sample of 40 people, the mean body mass index (BMI) was 26.9 and the standard deviation was 6.03. O A. Use a normal distribution because the sample is random, the population is normal, and is known O B. Use a...
Use the standard normal distribution or the t-distribution to construct the indicated confidence interval for the population mean of each data set. Justify your decision. If neither distribution can be used, explain why. Interpret the results. (a) In a random sample of 36 patients, the mean waiting time at a dentist’s office was 24 minutes and the standard deviation was 7.5 minutes. Construct a 90% confidence interval for the population mean. (b) In a random sample of 25 cereal boxes,...
Scores on the SAT mathematics section have a normal distribution with mean 4-500 and standard deviation o=100. a. What proportion of students score above a 550 on the SAT mathematics section? Round your answer to 4 decimal places. b. Suppose that you choose a simple random sample of 16 students who took the SAT mathematics section and find the sample mean x of their scores. Which of the following best describes what you would expect? The sample mean will be...
If we know the population standard deviation and we use the t-test instead of the Z-test, a) We will increase the probability of type II error. b) We will increase the probability of type I error. c) We will have the same conclusion d) None of the above The chi-square goodness-of-fit test can be used to test for: a) significance of sample statistics b) difference between population means c) normality d) probability
Use Excel to standard normal observations with assumed population parameters with mean 16 and standard deviation 5. Go to Data Analysis (you need to have chosen "Analysis Toolpack" first) -> Random Number Generation -> Normal. Generate one random variable with numbers generated for samples of size 5, 16, and 25 from the default standard normal distribution. This will simulate the importance of the "assume normal" assumption. Use the =) provided from the parent population as your "assumed" population standard deviation....