Mathematics, 09.11.2019 06:31 frisha

5. true or false. (a) all other factors remaining the same, increasing the sample size, n, will decrease the width of a con dence interval. (b) we expect 95% of all 95% con dence intervals for the population mean to contain the sample mean. (c) the t-distribution is symmetric and centered at the population mean . (d) the t-distribution is very similar to the standard normal distribution regardless of its degrees of freedom. (e) all other factors remaining the same, a 90% con dence interval for a population mean is narrower than an 95% con dence interval for the same . 1

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Answer from: dianamunoz580

a) True

b) True

c) True

d) False

e) False

Step-by-step explanation:

(a) All other factors remaining the same, increasing the sample size, n, will decrease the width of a confidence interval.

True. Confidence intervals are calculated by calculating margin of error (ME) around the mean using the formula

ME= $\frac{z*s}{\sqrt{N} }$ where

z is the corresponding statistic (z-score or t-score) s is the standard deviation of the sample(or of the population if it is known) N is the sample size

As the formula suggests, all other factors remaining the same, if we increase N, ME decreases.

b) We expect 95% of all 95% confidence intervals for the population mean to contain the sample mean.

True. This is what 95% confidence level assumes.

True.

(d) The t-distribution is very similar to the standard normal distribution regardless of its degrees of freedom.

False. As the degrees of freedom increases t-distribution resembles the standard normal distribution. For small sample sizes (<30), this is not true.

(e) All other factors remaining the same, a 90% confidence interval for a population mean is narrower than an 95% confidence interval for the same population

False. 90% confidence interval for a population mean is wider than an 95% confidence interval for the same population

Answer from: Quest

Intersecting secant-tangent theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.so to break it down: 1. pq acts as the tangent and ps as the secant with an intersection at p.sr = 21rp = 3x + 3pq = 4x + 4following to equation: tangent squared = the two segments multiplied by each otherso (4x + 4) ^ 2 = (3x + 3) • (21) simplifies to 16x^2 - 31x - 47 = 0 or (16x - 47)(x + 1) x = -1 or x = 47/162. pq acts as the tangent and ps as the secant with an intersection at p (again! )sr = 16rp = xpq = 15(15) ^ 2 = 16 • x225 = 16xx = 225/163. the interesting chords are proportional to each other so a ratio is possible to set up: ap dp 10 3 + x = = —— = pc pb 8 xcross multiple to get 10x = (3 + x)(8)x = 12

Answer from: Quest

answer: i don't understand. what are the options

step-by-step explanation:

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5. true or false. (a) all other factors remaining the same, increasing the sample size, n, will decr...

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