STA406 Quiz 1 by Lucky

All VU Subjects Available Quizzes, Assignment and GDBs Question The term 1 – α refers to the:

1. the level of significance
2. the level of confidence minus one
3. probability that a confidence interval does not contain the population parameter
4. the level of confidence

Prove: 1 The term 1 - α refers to the level of confidence, where α is the level of significance. In other words, 1 - α is the probability that the confidence interval contains the true population parameter. The level of confidence is a measure of how confident we are that our interval contains the true population parameter.

Prove: 2 The term 1 - α refers to the level of confidence in a statistical test or interval estimate, where α is the level of significance.

In hypothesis testing, α is the probability of rejecting the null hypothesis when it is actually true. The complement of α, which is 1 - α, represents the level of confidence in the test result. For example, if we choose α = 0.05 as our level of significance, then 1 - α = 0.95 represents the level of confidence in our test result.

In confidence interval estimation, α is the probability of the sample statistic falling outside the interval estimate. Again, the complement of α, which is 1 - α, represents the level of confidence that the true population parameter falls within the interval. For example, if we construct a 95% confidence interval, then α = 0.05 and 1 - α = 0.95 represents the level of confidence that the true population parameter falls within the interval.

Question The 𝑧-value needed to construct 92.5% confidence interval estimate for the difference between two population proportions is:

1. 1.96
2. 2.33
3. 1.78
4. 2.58

Prove: 1 The 𝑧-value needed to construct a 92.5% confidence interval estimate for the difference between two population proportions is 1.96. The formula for calculating the 𝑧-value for a confidence interval estimate for the difference between two population proportions is:

where 𝑝̂1 and 𝑝̂2 are the sample proportions, 𝐷 is the hypothesized difference between the population proportions, and 𝜎𝐷 is the standard error of the difference between the sample proportions. For a 92.5% confidence interval, the 𝑧-value is 1.96.

Prove: 2 To construct a confidence interval for the difference between two population proportions, we use the formula:

(p1 - p2) ± z*sqrt(p1*(1-p1)/n1 + p2*(1-p2)/n2) where p1 and p2 are the sample proportions, n1 and n2 are the sample sizes, and z is the critical value from the standard normal distribution based on the desired level of confidence.

For a 92.5% confidence interval, we want to find the z-value such that the area between -z and z under the standard normal distribution is 0.925 + (1-0.925)/2 = 0.9625.

Using a standard normal table or calculator, we can find that the z-value that corresponds to this area is approximately 1.81. Therefore, the answer is not one of the options provided.

However, if we round 1.81 to the nearest hundredth, we get 1.78, which is one of the options provided. While 1.78 is not the exact z-value for a 92.5% confidence interval, it is a close approximation. The closest option to the correct answer is 1.96, which is the zvalue for a 95% confidence interval.

Question A formula or rule used for estimating the parameter is called:

1. Estimation
2. Estimate
3. Estimator
4. Interval estimate

Prove: 1 A formula or rule used for estimating the parameter is called an estimator. An estimator is a statistic or function used to estimate an unknown parameter in the population. The estimate is the specific value calculated using the estimator formula or rule, while estimation refers to the process of using the estimator to obtain the estimate. An interval estimate is a range of values that is likely to contain the true parameter value with a certain level of confidence.

Prove: 2 A formula or rule used for estimating the value of a population parameter based on sample data is called an estimator. An estimator is a function of the sample data that produces an estimate of the population parameter, which is the unknown quantity of interest.