Finding Correct Z and T Scores for Confidence Intervals

Finding appropriate z- and t-scores is important when constructing confidence intervals. Confidence intervals allow one to estimate important population parameters such as population mean, population proportion, population standard deviation, etc. We will also study how confidence intervals will let one determine how large of a sample is required in order to get within a desired error range. Thus, confidence intervals offer important real-world applications. In Part 4 of this lab (described below) you will use a population mean confidence interval to determine if the local economy is sufficient to handle a new candy-making business.

Part 3, however, focuses on finding the correct z- and t-scores for a given confidence level. You should carefully follow the examples located inside the Conf Intervals worksheet in our Lab 6 Excel file (linked above or here). Then, answer the following questions. Note that these questions are also inside the worksheet.

1. Using Excel, find the z-score that corresponds to the following Confidence Levels:

a. 80%
b. 85%
c. 92%
d. 97%

2. Using Excel, find the t-score that corresponds to the following Confidence Levels and Sample Sizes:

a. 95% with n = 25
b. 96% with n = 15
c. 97% with n = 21
d. 91% with n = 10

Solution Preview

(1)We use the excel formula -NORMSINV

(a) -NORMSINV((1 - 0.80)/2) = 1.2816

(b) -NORMSINV((1 ...

Solution Summary

A Complete, Neat and Step-by-step Solution is provided.

Suppose that, for a sample size n = -100 measurements, we find that x = 50. Assuming that the standard deviation equals 2, calculate confidenceintervalsfor the population mean with the following confidence levels:
a) 95% b) 99% c) 97% d) 80% e) 99.73% f) 92%

Using the spread sheet that is attached, develop 95% and 99% confidenceintervalsfor the following:
The mean hours per week that individuals spend in their vehicles,the average number of miles driven per week, the proportion of individuals who are satisfied with their vehicle and the proportion of individuals who have at least

A cutoff score of 79 has been established for a sample of scores in which the mean is 65. If the corresponding z-score is 1.4 and the scores are normally distributed, what is the standard deviation?

The following sample information is given concerning the ACT scores of high school seniors form two local schools.
School A School B
n1 = 14 n2= 15
x1 = 25 x2 = 23
var1 = 16 var 2 = 10
Develop a 95% confidence interval estimate for the difference between the two populations.

1. What is the 99% confidence interval for the variance of exam scoresfor 25 algebra students, if the standard deviation of their last exam was 10.7?
2. In a sample of 60 mice, a biologist found that 42% were able to run a maze in 30 seconds or less. find the 98% limit for the population proportion of mice who can run that m

1. Why are confidenceintervals useful?
2. You and a colleague conducted a study on grocery totals for shoppers in the State of Michigan. Your estimated grocery totals at CI 95%: ($78, $98). In writing the report, your colleague stated: "There is a 95% chance that the true value of ยต will fall between $78 and $98.
a.

Assume that in a hypothesis test with null hypothesis H 0: mu = 14.0 at alpha = 0.05, that a value of 13.0 for the sample mean results in the null hypothesis being rejected. That corresponds to a confidence interval result of:
a) the 95% confidence interval for the mean contains the value 14.0
b) the 95% confidence interval

ConfidenceIntervalsfor the Mean (Large Samples)
Find the critical value zc necessary to form a confidence interval at the given level of confidence. (References: definition for level of confidence
a. 95%=
b. 75%=