A 95% confidence interval contains 5. If the confidence level is increased to 99%, will the...

A 95% confidence interval contains 5. If the confidence level is increased to 99%, will the new interval contain 5?

		Yes
		No
		Unable to determine

Expert Solution

The correct option is: Yes [ANSWER]

Explanation:
For the same data, if we construct two confidence intervals at two different confidence levels, then all the points containted in the confidence interval with lower confidence level are also contained in the confidence interval with the higher confidence level.

This is because, for the same set of data, as we increase the confidence level, the confidence interval 'expands' from both sides. This is because as we increase the confidence level we are in effect increasing the probability that confidence interval 'captures' the true value of the parameter, which is achieved by expanding the confidence interval.

Thus, a confidence interval with lower confidence level is in fact a subset of the confidence interval with higher confidence.

[Note that this is true only if it is applied to the same data]

Thus, a point that lies in the 95% confidence interval will also lie in the 99% confidence interval.

Thus, if a 95% confidence interval contains 5, then if the confidence level is increased to 99%, the new interval will also contain 5.

For any queries, feel free to comment and ask.

If the solution was helpful to you, don't forget to upvote it by clicking on the 'thumbs up' button.

orchestra answered 2 years ago

At a confidence level of 95% a confidence interval for a population proportion is determined to...

At a confidence level of 95% a confidence interval for a population proportion is determined to be 0.65 to 0.75. If the sample size had been larger and the estimate of the population proportion the same, this 95% confidence interval estimate as compared to the first interval estimate would be A. the same B. narrower C. wider

Calculate the 99%, 95%, and 90% confidence interval for the following information. Identify how these confidence...

Calculate the 99%, 95%, and 90% confidence interval for the following information. Identify how these confidence intervals are similar and how they are different. Explain why. (70 points) x̄ = 55 s = 15 n = 101 The 99% Confidence Interval: The 95% Confidence Interval: The 90% Confidence Interval: Similarities: Differences: Why?

1. If you decrease the level of confidence from 99% to 95%, the width of confidence...

1. If you decrease the level of confidence from 99% to 95%, the width of confidence interval will A. increase by 4% B. decrease by 4% C. decrease by 8% D. None of the above 2. If you wish to decrease the margin of error, you may do which one of the following: A. Increase the sample size. B. Reduce the population size. C. Decrease the level of confidence. D. Both b and c E. Both a and c 3. In...

A confidence interval, at the 95% confidence level, will be used to answer the question, "What...

A confidence interval, at the 95% confidence level, will be used to answer the question, "What is the mean annual salary (in US dollars) of a Tesla car owner?" Data was collected from 36 Tesla owners across the US. The mean annual salary of those 36 Tesla owners was $254000. The standard deviation of ALL Tesla owners is known to be $1057. a) The value at the center of the confidence interval represents what quantity? Choose an option from the list and type its...

Multiple choice 1.If a confidence interval is constructed at a confidence level of 99% instead of...

Multiple choice 1.If a confidence interval is constructed at a confidence level of 99% instead of 95% a.Estimation precision decreases b.The precision of the estimate is not altered c.Estimation accuracy improves significantly d.We can accurately calculate the value of the parameter of interest 2.The confidence level in a confidence interval represents: a.The probability that that particular interval contains the true value of the parameter b.How sure we are of having correctly estimated the parameter c.None of the options exposed d.The...

Problem: Construct and interpret a 90%, 95%, and 99% confidence interval for the mean heights...

Problem: Construct and interpret a 90%, 95%, and 99% confidence interval for the mean heights of either adult females or the average height of adult males living in America. Do not mix genders in your sample as this will skew your results. Gather a random sample of size 30 of heights from your friends, family, church members, strangers, etc. by asking each individual in your sample his or her height. From your raw data convert individual heights to inches....

If the confidence level is increased from 90% to 99% for a simple random sample of...

If the confidence level is increased from 90% to 99% for a simple random sample of size n, the width of the confidence interval for the mean μ will: Question 1 options: The answer cannot be determined from the information given. decrease. stay the same. increase.

Construct a confidence Interval for p1- p2, at a 95% level of confidence, if x1= 366,...

Construct a confidence Interval for p1- p2, at a 95% level of confidence, if x1= 366, n1=535, x2=435, n2=593

Find the 80%, 95%, and 99% confidence intervals & margin error Create your own confidence interval...

Find the 80%, 95%, and 99% confidence intervals & margin error Create your own confidence interval (you cannot use 80%, 95%, and 99%) and make sure to show your work. Make sure to list the margin of error. 122 132 97 102 106 116 94 132 112 123 123 108 84 120 125 123 115 103 127 139 122 124 112 113 109 104 120 109 117 108 125 109 119 138 125 104 110 101 130 124 115 104...

IF the 95% confidence interval does not contains the hypothesised parameter, then a hypothesis test at...

IF the 95% confidence interval does not contains the hypothesised parameter, then a hypothesis test at the 0.05 level will almost always reject the null hypothesis in a two-tailed test? do you agree with this statement? explain.

Question