CNSL503 / CNSL 503 Module 5 Statistics Exam 2026/2027 | Practice Questions & Accurate Solutions

CNSL503 / CNSL 503 Module 5 Statistics Exam 2026/2027 | Practice Questions & Accurate Solutions Q: What would be a valid statement regarding a 95% confidence interval for the unknown mean of a population. Answer We are 95% confident that the unknown population mean is contained in the interval. Q: What would be a valid statement regarding a 95% confidence interval for the unknown mean of a population. Answer 95% of the confidence intervals calculated using this method will contain the true population mean. Q: What would be a valid statement regarding a 95% confidence interval for the unknown mean of a population. Answer If you produced 100 confidence intervals using the same method, we would expect that approximately 95 of them will contain the true population mean. Q: What would be a valid statement regarding a 95% confidence interval for the unknown mean of a population. Answer The method used to generate this interval will correctly generate other intervals that contain the true population mean 95% of the time. Q: A t-distribution has thicker tails than a normal distribution. Answer True Q: There is more probability in the tails for a normal distribution. Answer False Q: As n increases the t-distribution approaches the standard normal distribution. Answer True Q: As n increases, the tails in the t-distribution become "fatter". Answer False Q: The shape of a t-distribution depends on its degrees of freedom. Answer True Q: We will always use a student's t distribution when we are given raw data to analyze, regardless if we know the population standard deviation or not. Answer False Q: We use the Student's t-distribution when we estimate the mean of a population that is normally distributed, has an unknown standard deviation, and small n. Answer True Q: t-distributions are similar in shape to the standard normal curve. Answer True Q: If we were to compute a 95% confidence interval using the Student's t distribution for a population of interest using a random sample of size n, how would the following impact the confidence interval? Answer - If n were to increase, the size of our interval would decrease Q: If we were to compute a 95% confidence interval using the Student's t distribution for a population of interest using a random sample of size n, how would the following impact the confidence interval? Answer - If n were to decrease, the size of our interval would increase Q: If we were to compute a 95% confidence interval using the Student's t distribution for a population of interest using a random sample of size n, how would the following impact the confidence interval? Answer - If it were constructed using a higher confidence level, the size of our interval would increase Q: If we were to compute a 95% confidence interval using the Student's t distribution for a population of interest using a random sample of size n, how would the following impact the confidence interval? Answer - If it were constructed using a lower confidence level, the size of our interval would decrease Q: If we were to compute a 95% confidence interval using the Student's t distribution for a population of interest using a random sample of size n, how would the following impact the confidence interval? Answer - If we had a larger sample standard deviation, the size of our interval would increase Q: If we were to compute a 95% confidence interval using the Student's t distribution for a population of interest using a random sample of size n, how would the following impact the confidence interval? Answer - If we had a smaller sample standard deviation, the size of our interval would decrease Q: If we were to compute a 95% confidence interval using the Student's t distribution for a population of interest using a random sample of size n, how would the following impact the confidence interval? Answer - If we used the same sample but knew the population standard deviation, the size of our interval would decrease Q: A random sample of 35 Airbus jet planes have a mean speed of 740 mph with a standard deviation of 57 mph. A random sample of 38 Boeing 747 jet planes have a mean speed of 898 mph with a standard deviation of 44 mph. Do Boeing 747 jet planes tend to have a higher mean speed than the Airbus jet planes? Answer - what is the appropriate confidence interval? two sample T-interval Q: A random sample of 35 Airbus jet planes have a mean speed of 740 mph while a random sample of 38 Boeing 747 jet planes have a mean speed of 898 mph. The standard deviation for both aircrafts are known to be 57 mph and 44 mph, respectively. Do Boeing 747 jet planes tend to have a higher mean speed than the Airbus jet planes? Answer - what is the appropriate confidence interval? two sample Z-interval Q: A random sample of 54 hot dog stands were sampled to determine the mean price of hot dogs in New York. The selected stands had a mean price $4.51 per hot dog and a standard deviation of $0.43 per hot dog. Find a 90% confidence interval for the true mean price of hot dogs in New York. Answer - what is the appropriate confidence interval? one sample T-interval Q: A random sample of 36 apple trees were sampled to determine the average yielding an apple orchard. The average yield was 834 pounds per tree. The population standard deviation for this particular species of tree is 113 pounds. Find a 95% confidence interval for the mean weight of apples produced. Answer - what is the appropriate confidence interval? one sample Z-interval Q: Two truck dealerships, Peterbilt and Kenworth, have both launched the same new warranty program for their customers. Peterbilt had 352 of the 891 customers purchase the warranty while Kenworth had 226 of their 578 customers purchase the warranty. At the 95% confidence level, are Peterbilt customers more likely to purchase the warranty than Kenworth customers. Answer - what is the appropriate confidence interval? two sample P-interval Q: A recent flyer claimed that 2 out of every 9 trucks sold at a local dealership are manufactured by Peterbilt. Find a 95% confidence interval for those who shop at this dealership that will purchase a Peterbilt truck. Answer - what is the appropriate confidence interval? one sample P-interval Using the z-test requires that we know... standard deviation When the standard deviation is unknown, we estimate it using... Answer the sample standard deviation (s) When we use s instead of σ, the distribution of the sample means is no longer ____. Answer normal Instead of the normal distribution, the distribution of sample means when σ is estimated using s follows a... Answer t distribution (aka student distribution) The t distribution is... Answer symmetrical with most scores centered around the mean The shape of the t distribution changes depending on the... Answer degrees of freedom degrees of freedom Answer the number of scores in the sample that are independent degrees of freedom formula Answer df= n-1 As sample size increases, degrees of freedom ____ and the variability in sample means ____. increases, decreases one sample t-test compares one sample mean against the population mean How many critical values are there for a 2-tailed test? 2; one positive and one negative How many critical values are there for a 1-tailed test? 1; it may be positive or negative t-test statistic formula t=(X̄- μ)/s(X̄) s(X̄)= s/squareroot(n) It is generally easier to reject the null hypothesis with... one tailed tests 2 tailed tests are more common for more ____ tests stringent confidence interval for one sample t-test formula CI(1-α)= X̄ +/- tcrit (s/squareroot(n)) cohen's d for one sample t-test formula d= (X̄- μ)/s independent measures design aka between subjects design; compares different treatments where each participant is in only one treatment group Independent measures design compares samples from different... existing populations repeated measures design aka within subjects design; compares treatments by having each participant undergo every treatment level example of a related measures design low fat diet -- weight loss -- low carb diet -- weight loss pro of independent measures design each participant receives only 1 tx con of independent measures design more variability, making it more difficult to detect real effects pro of repeated measures deisgn less variability, making it easier to detect real effects con of repeated measures design each participant goes through all the txs counterbalancing example low fat diet-- weight loss -- low carb diet -- weight loss low carb diet -- weight loss-- low fat diet -- weight loss matched pairs study matches participants in different tx groups on specific characteristics Matched pairs study is an example of... a related samples design problem with matched pairs study if one of the matched pair drops out, the results from the other matched participant cannot be used independent samples t-test compares 2 samples that are distinct and independent of one another The 2 samples may be... 2 separate tx groups or 2 groups based on 1 existing characteristic The independent samples t-test is a test of the... difference between 2 means degrees of freedom for independent samples t-test formula df total= n1 - n2 -2 σX̄ standard error of the distribution of sample means (X̄) that is a z dsitriubution sX̄ standard error of the distribution of sample means (X̄) that is a t distribution s(X̄1-X̄2) standard error of the distribution of the difference between sample means (X̄1-X̄2) that is a t distribution independent measures t statistic formula t= (X̄1-X̄2)/s(X̄1-X̄2) s(X̄1-X̄2) formula if n1=n2 s(X̄1-X̄2)= squareroot((s1)^2/n1 + (s2)^2/n2) pooled variance sp^2 formula sp^2= ((df1)(s1)^2)/df(total) +((df2)(s2)^2)/df(total) s(X̄1-X̄2) formula if n1 does not equal n2 s(X̄1-X̄2)= squareroot ((sp^2/n1) + (sp^2/n2)) 3 steps of calculating independent measures t statistic 1. calculate the pooled variance 2. calculate the standard error 3. calculate the t statistic confidence interval for independent measures t statistic formula CI(1-α)= (X̄1-X̄2) +/- tcrit (s(X̄1-X̄2)) cohen's d formula for independent measures t statistic d= (X̄1-X̄2)/ squareroot(sp^2) paired samples t-test compares 2 samples that are related to one another The paired samples t-test is a test of the.... difference between 2 related means formula for paired samples t-test t= X̄D/sX̄D or X̄D/sD/squareroot(n) formula for paired samples t-test standard error sX̄D= squareroot(sD^2/n) or sD/squareroot(n) sD^2= Σ(D-X̄D)^2/n-1 confidence interval formula for paired sample t-test CI(1-α)= X̄D +/- tcrit(sX̄D) cohen's d formula for paired sample t-test d= X̄D/sD