Unit 6 Practice Test - Inference for Means - Part VI

Sep 30, 2026

Practice test covering inference for means in Unit 6, focusing on comparing t-distributions with the normal distribution, interpreting confidence intervals for a mean, computing the standard error of a sample proportion, forming t-based confidence intervals for an unknown mean with sample standard deviation, and assessing hypotheses with p-values and one- vs two-tailed tests. Additional items address why certain t procedures are inappropriate for non-random or complete populations, effects of increasing sample size, pooled variance/standard deviation calculations, and recognizing Type II errors.

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Unit 6 Practice Test - Inference for Means - Part VI

Multiple-Choice Questions

# Unit 6 Practice Test-Inference for Means-Part VI Name _1.Which statement correctly compares t-distributions to the normal distribution? I.t distributions are also mound shaped and symmetric. I.t distributions have less spread than the normal distribution.IⅢ.As degrees of freedom increase,the variance of t distributions becomes smaller. A)I only B)Ⅱ only C)I and II only D)I and II only E)I,II,and I 2.A marketing company reviewing the length of television commercials monitored a randomsample of commercials over several days.They found that a 95%confidence interval for themean length (in seconds)of commercials aired daily was(23,27).Which is true? A)95%of the commercials they checked were between 23 and 27 seconds long. B)95%of all the commercials aired were between 23 and 27 seconds a day. C)Commercials average between 23 and 27 seconds long on 95%of the days. D)95%of all samples would show mean commercial length between 23 and 27 seconds. E)We’re 95%sure that the mean commercial length is between 23 and 27 seconds. _3.A random sample of 120 classrooms at a large university found that 70%of them had beencleaned properly.What is the standard error of the sample proportion? D)0.082 E)0.458C)0.046B)0.042A)0.028 4.A coffee house owner knows that customers pour different amounts of coffee into their cups.She samples cups from 10 costumers she believes to be representative of the customers andweighs the cups,finding a mean of 12.5 ounces and standard deviation of 0.5 ounces.Assuming these cups of coffee can be considered a random sample ofall cups of coffeewhich of the following formulas gives a 95%confidence interval for the mean weight of allcups of coffee? 5.Doctors at a technology research facility randomly assigned equal numbers of people to usecomputer keyboards in two rooms.In one room a group of people typed a manuscript usingstandard keyboards,while in the other room people typed the same manuscript usingergonomic keyboards to see if those people could type more words per minute.Aftercollecting data for several days the researchers tested the hypothesis H₀:H-μ₂=0 againstthe one-tail alternative and found P=0.22.Which is true? A)The people using ergonomic keyboards type 22%more words per minute. B)There's a 22%chance that people using ergonomic keyboards type more words perminute. C)There's a 22%chance that there's really no difference in typing speed. D)There's a 22%chance another experiment will give these same results. E)None of these. 6.An elementary school principal wants to know the mean number of children in familieswhose children attend this school,He checks all the families using the school's registrationrecords,and we use the TI-83 to create a 95%confidence interval based on a t-distribution.This procedure was not appropriate.Why? A)Since these families are from only one school,the family sizes may be skewed. B)The entire population of families was gathered so there is no reason to do inference. C)The recent record-setting family with twelve children is probably an outlier D)The population standard deviation is known,so he should have used a z-model. E)At a given school families are not randomly selected. __7.Trainers need to estimate the level of fat in athletes to ensure good health.Initial tests werebased on a small sample but now the trainers double the sample size for a follow-up test.Themain purpose of the larger sample is to.. A)reduce response bias.B)decrease the variability in the population. C)reduce non-response bias.D)reduce confounding due to other variables. E)decrease the standard deviation of the sampling model. 8.Based on data from two very large independent samples,two students tested a hypothesisabout equality of population means using α=0.02.One student used a one-tail test andrejected the null hypothesis,but the other used a two-tail test and failed to reject the null.Which of these might have been their calculated value of t? A)1

FAQs

How should t-distributions compare to the normal distribution as degrees of freedom increase?

As degrees of freedom increase, the t-distribution approaches the normal distribution. It becomes more similar in shape and spread as df grows.

How do you interpret a confidence interval for the mean length of commercials?

A 95% confidence interval represents a range of plausible values for the population mean. It is not the same as saying 95% of individual commercials fall inside the interval.

Why can a t-based confidence interval procedure be inappropriate when families are not randomly selected?

If families are not randomly selected, the sampling distribution assumptions for t inference do not hold. The resulting interval may not reflect correct coverage for the intended population.

Sep 30, 2026

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