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An in-depth exploration of confidence intervals and hypothesis testing, focusing on the calculation of standard deviations, margin of errors, and degrees of freedom for various sample sizes and population parameters. It covers topics such as point estimates, normal and t distributions, and the construction of confidence intervals and tolerance intervals for population means and proportions.

Typology: Exams

2023/2024

1 / 83

Download Statistical Inference: Confidence Intervals and Hypothesis Testing and more Exams Nursing in PDF only on Docsity! 1 Chapter 7 Sampling Distributions If the population from which a sample is drawn is normally distributed then the sampling distribution of the sample mean is normally distributed A theorem that allows us to use the normal probability distribution to approximate the sampling distribution of the sample mean whenever the sample size is large is known as The central limit theorem As a general guideline the normal distribution approximation can be used to describe the sampling distribution of the 2 sample mean when The central limit theorem states that the distribution of the sample mean will be approximately normal if the sample size is sufficiently large as a general guideline The central limit theorem states that for any distribution as n gets larger the sampling distribution of the sample mean becomes closer to a normal distribution Suppose we choose a sample of size 100 from a population of monthly cable bills having a standard deviation of $20. If we assume the population mean bill is $65 what is the probability mean of our sample is greater than The central limit theorem states that the distribution of the sample mean will be approximately normal if the sample The probability distribution describing the set of all possible values of S2 is called Consider a population having mean u=100 If u is an unbiased point estimate of u then the mean of u Suppose you choose a sample of size 100 from a population having 25% successes the sample proportion of successes will have standard deviation suppose you choose a sample of size 16 a 95% confidence interval for the population mean implies that if samples are drawn repeatedly and confidence intervals for u are constructed then which of the following is the correct formula for the margin of error in the interval estimation of p When the population standard deviation is unknown the standard error for the sample mean is calculated as A random sample of size 400 is taken from a population whose population proportion is 0.25 the expected value of the sample proportion is As the sample size increases the shape of the sampling distribution of p becomes more normal The standard deviation of the sampling distribution of x is equal to If we were to sample repeatedly from a population having mean = 10 and standard deviation = 2 A random sample of size 400 is taken from a population whose population proportion is 0.25 the expected value of the The standard deviation of p equals If we assume that a population has proportion p=0.2 and we choose a random sample of size 400 what is the chance the sample proportion p is greater than or equal to 0.25 a population has a mean of 100 and a standard deviation of 12 a population has a mean of 100 and a standard deviation of 10 a random sample of size 100 is taken from a population Suppose you choose a sample of of size 100 from a population having 25% successes Chapter 8 Confidence Intervals In order to construct a confidence interval for u the sampling distribution of the estimator x must follow or approximately follow a(n) distribution A confidence interval narrows if the following is accomplished True or false for a given sample size n and population standard deviation o the lower the confidence level 100 (1-x)% a random sample of size 100 is taken from a population Regardless of the sample size the estimator x follows a normal distribution when the underlying population follows a which of the following statements about the degrees of freedom of a t distribution are true A type I error occurs when we reject a null hypothesis that is Which of the following hypothesis tests are two tailed Regardless of the sample size the estimator x follows a normal distribution when the underlying population follows a the critical value of a less than hypothesis test is the critical value of a greater than hypothesis test is Suppose we wish to derive a confidence interval for the mean of a right skewed population In order to derive a valid confidence interval for u x must be based on a sample which If a equals 0.05 then the confidence level equals 0.95 A confidence interval can be interpreted as a Suppose you have a random sample from a population whose standard deviation o is known What is the confidence level if x=.10 A 95% confidence interval for the population mean is constructed at 6+/-2 what is the confidence coefficient A 95% confidence interval for the population mean is constructed at 6+/-2 what is the margin of error A 95% confidence interval for the population mean is constructed at 6+/-2 what is the probability of error A 95% confidence interval for the population mean is constructed at 6+/-2 what is the A 95% confidence interval for the population mean is calculated as [40, 80] the point estimate for u is For a 95% confidence interval A = 0.05 which of the following is a valid form of a confidence interval suppose you are constructing a confidence interval for the population mean for a given confidence level and standard deviation Suppose you are constructing a confidence interval for the population mean for a given sample size and population standard deviation how will the width of the interval change as the confidence level increases Suppose you are constructing a confidence interval for the population mean for a given confidence level and sample size the width of the interval is wider for a Suppose you are constructing a confidence interval for the population mean for a given sample size and standard deviation the width of the interval is wider for a A sample of 25 is drawn from a normal population with an unknown population standard deviation. The sample mean and the sample standard deviation are calculated as 35 and 100 A sample of 25 is drawn from a normal population with a population standard deviation of 100 Suppose the mean of the sample is x = 35 suppose in a preliminary sample size of n = 20 you find s = 12.85 how large a sample should you choose if you wish to construct a 95% if the population standard deviation is unknown and we wish to calculate the sample size required to ensure our confidence interval has margin of error E we must when the population standard deviation is unknown the standard error for the sample mean is calculated as suppose in a preliminary sample size of n = 20 you find s = 12.85 how large a sample should you choose if you wish to A sample of 16 is drawn If samples of size n are drawn repeatedly from a given population and each sample is used to construct a 95% As the degrees of freedom increase the t distribution becomes more A sample size 25 is drawn from a normal population suppose the sample mean x = 50 and that the margin of error for a 95% confidence interval is 10 A 95% confidence interval for the mean is Suppose a standard error of x is .10 and s = 0.30 The sample size must be how is a confidence interval for the mean different from a point estimate of the mean suppose we choose a sample of size 10 from a normally distributed population The most practical way to reduce the margin of error is by When the confidence level increases form 95% to 99% the confidence interval for the population mean When examining the possible outcome of an election what type of confidence interval is most suitable for estimating the current support for a candidate If sample size n are drawn repeatedly from a given population and each sample is used to construct a 95% confidence interval for u the value of t.50 is suppose we use the same data set to construct a 95% tolerance interval and a 95% confidence interval suppose that in a preliminary sample of size n=20 you find s=12.85 how large a sample should you choose if you wish to construct a 95% confidence interval for u having margin of error 2.5 the sample size formula for estimating a proportion using a confidence interval with margin of error E involves the product A 100(1-a)% confidence interval for the population proportion is If the population standard deviation is unknown and we wish to calculate the sample size required to ensure our confidence interval has a margin of error E we must when constructing a confidence interval for the population mean the factors that affect the width of the confidence A t distribution the p is used as the point estimator of the p suppose you are interested in designing a medical device that will fit comfortably on the wrists of 99% of all adult patients to do this should you be interested in a 99% tolerance interval for wrist sizes or a 99% confidence interval for the mean wrist size A t distribution If a 95% tolerance interval for the actual weight of sacks of sugar Arrange the steps from first to last of hypothesis testing using the p value rule The null hypothesis denoted Ho, is the statement given the benefit of the doubt Match Match Match Order True or false for a given sample size n the chances of a type I error can only be reduced at the expense of a higher chance of Type II error True or false if [4,9] is a 95% confidence interval for o2 then Match
True or false: If [4, 9] is a 95% confidence interval for 07, then [2, 3] is a 95% confidence interval
foro.
% sorry, your answer is incorrect.
Missed!
v True
False
Suppose you hope to establish that a population mean exceeds 100. You should use
Hj: 100 andH,: 1 __ 100.
Your answer is correct.
Suppose we wish to test Hou = 100
Suppose we wish to test Hou = 100 Hou = 100 Suppose the competing hypothesis for a test are Hou = 10 Suppose you wish to test Hoo2 = .01 suppose [21.56 Suppose you wish to test Hoo2 = .01 Suppose you wish to test Hoo2 less than or equal to .01 Suppose the consequences of a Type I error are very serious which of the following values would be the most In a less than hypothesis test the null hypothesis is rejected if an only if Using the provided t table find the t point that gives a right hand tail area of In which of the following situations would we use a z test based on a proportion Suppose we want to test the claim that the proportion of a population is less than 50% Suppose we want to test the claim that the proportion of a population is more than 80%. A sample of 1000 Suppose we want to test the claim that the mean of a population is less than 20. pvalue Suppose we want to test the claim that the mean of a population is less than 20. Test statistic Suppose we want to test the claim that the mean of a population is less than 80. Test statistic Suppose we want to test the claim that the mean of a population is not equal to 40 positive critical value Suppose that we want to test the claim that the mean of a population is greater than 20. pvalue Suppose that we want to test the claim that the mean of a population is not equal to 40 pvalue Suppose that we want to test the claim that the mean of a population is not equal to 40 also suppose that the population standard deviation is known to be 18 test statistic Suppose that we want to test the claim that the mean of a population is less than 80 also suppose Suppose that we want to test the claim that the proportion of a population is less than 50% Suppose that we want to test the claim that the proportion of a population differs from 30% Consider a chi-square curve with 14 degrees of freedom Consider a chi-square curve with 8 Coffee urns As our pvalue decreases how does our evidence against the null hypothesis change In hypothesis testing what are the two incorrect decisions possible When the null hypothesis is tested, a decision is either correct or incorrect. An incorrect decision can be made in two ways: We can reject the null hypothesis when it is true (Type I error) or we can fail to reject the null hypothesis when it is false (Type II error). In the hypothesis test of Hou Which of the following statements are true Which of the following will help reduce the probability of committing a type II error The critical values of a “not equal to” hypothesis test are In a greater than hypothesis test the null hypothesis is reject if an only if Hou = 3 Hou less than or equal to Which of the following will help reduce the probability of committing a type II error Suppose you wish to calculate B the probability of a type II error when you perform a level a An automobile parts supplier will modify its process if the diameters of its cylindric engines are not 3 What is B the probability of a Type II error corresponding to the alternative value ua Assume the test is one-tailed under what circumstances do we reject a null hypothesis Assume that Ho is u less than 5 and Ha is u True or false the probability of a Type II error is the same for all possible values of u True or false if the sample size is large the t test is valid even if the sampled population is not normally distributed the power of a statistical test is measured by under what circumstances do we reject a null hypothesis The power of a statistical test is defined as the probability of rejecting