Mathematics, 03.02.2020 01:56 dstyle

What is the z-score with a confidence level of 95% when finding the margin of error for the mean of a normally distributed population from a sample? 0.99 1.65 1.96 2.58

Answers: 1

Show answers

Answers

Answer from: hiji0206

For a confidence interval of 95%, z is 1.96

Step-by-step explanation:

A z-score, also called as standard score, indicates how many standard deviations away an element is from the mean. z-score can be calculated from the following formula,

$z=\dfrac{X-\mu}{\sigma}$

where,

X = Raw score,

μ = mean,

σ = standard deviation.

For a confidence interval of 95%, we take z as 1.96

Answer from: elizabethivy75

1.96

Further explanation

We will answer what is the value of the Z-score with a confidence level of 95% when finding the margin of error for the mean of a normally distributed population from a sample.

Z represents the value from the standard normal distribution for the selected confidence level.

See below, Z-scores for commonly used confidence intervals.

Desired Confidence Interval = 90%, with Z-score = 1.645Desired Confidence Interval = 95%, with Z-score = 1.96Desired Confidence Interval = 99%, with Z-score = 2.576

Thus, the Z-score with a confidence level of 95% is $\boxed{\boxed{ \ Z = 1.96 \ }}$

Notes:

A confidence level of 95% (or confidence intervals) mean that if we take 100 different samples and calculate 95% confidence intervals for each sample, then about 95 out of 100 confidence intervals (CI) will contain the true mean value (μ).

In practice, we choose a random sample and produce a confidence interval, which may or may not contain the true mean. The observed interval may be more or less than μ. As a result, 95% CI represents the range of possible precise and unknown parameters.

The formulas for confidence levels for the population mean depend on the sample size and are given below.

Confidence Intervals for μ

For n ≥ 30, $\boxed{ \ X = \pm Z \bigg( \frac{s}{\sqrt{n}} \bigg) \ }$ . We use the Z table for the standard normal distribution.For n < 30, $\boxed{ \ X = \pm t \bigg( \frac{s}{\sqrt{n}} \bigg) \ }$ . We use the t table with df = n - 1

With,

μ = the population meann = the sample sizeX = the sample means = the standard deviationdf = degree of freedom

In general, the relationship between the margin of error and the sample size is as follows:

The margin of error will be very small due to the large sample size. The margin of error will be greater due to the small sample size.Learn moreEvaluate a combination and a permutation Which graph represents the sequence The derivatives of the composite function

Keywords: what is the z-score, with, a confidence level, 95%, when, finding, the margin of error, for, the mean, a normally distributed population, from a sample, 0.99, 1.65, 1.96, 2.58, the sample size, mean, standard deviation, statistics, probability

Answer from: Quest

As you know john locke said he wanted life liberty and the pursuit of happiness so thomas jefferson was inspired about what john locke said so thomas jefferson wrote the declaration of independence for people to be free for people to be happy

Answer from: Quest

step-by-step explanation: