Assuming a sample size of 31: a) What t-scores isolate the middle 95% of the population?...

Assuming a sample size of 31:
1. a) What t-scores isolate the middle 95% of the population?
2. b) What t-scores isolate the middle 99% of the population?
Assuming a sample size of 22:
1. a) What t-scores isolate the middle 95% of the population?
2. b) What t-scores isolate the middle 99% of the population?

Solutions

Expert Solution

$P(t > b) = 0.025 \\ or,\ P(t > b) = P(t > 2.042) \hspace{10 mm}[$ From t table with one tail probability \\ \hspace*{60 mm} of 0.025 and df = 30 $] \\ or, b = 2.042 \\\\ $ As, t distribution is symmetric about t = 0, so a = -2.042 $ \\\\ $ So, the scores of $ \mathbf{-2.042\ and\ 2.042} $ isolate the middle 95\% of the population $$

$P(t > b) = 0.025 \\ or,\ P(t > b) = P(t > 2.080) \hspace{10 mm}[$ From t table with one tail probability \\ \hspace*{60 mm} of 0.025 and df = 21 $] \\ or, b = 2.080 \\\\ $ As, t distribution is symmetric about t = 0, so a = -2.080 $ \\\\ $ So, the scores of $ \mathbf{-2.080\ and\ 2.080} $ isolate the middle 95\% of the population $$

orchestra answered 1 year ago

Next > < Previous

Related Solutions

What are the z-scores that mark the middle 95% of this distribution? What is the raw...

What are the z-scores that mark the middle 95% of this distribution? What is the raw score associated with the z-score below the mean calculated in the above question? What is the raw score associated with the z-score above the mean calculated in the 1st question? What is the median of this z-score distribution

What two z scores cut off the middle 95% of the normal distribution?

fine the t score with a 95% confidence level for a sample size of 19.

Assuming the sample size is 30, the sample mean (X) is 24.75, the population standard deviation...

Assuming the sample size is 30, the sample mean (X) is 24.75, the population standard deviation (σ) is 5, a 95% confidence interval for the population mean would have lower bound of _________________ and upper bound of _______________________.

Assuming the population has an approximate normal distribution, if a sample size n=10 has a sample...

Assuming the population has an approximate normal distribution, if a sample size n=10 has a sample mean ¯x=36 with a sample standard deviation s=9, find the margin of error at a 90% confidence level. THEN YOU MUST ROUND ANSWER TO TWO DECIMALS PLACES.

[t-interval] If sample mean = 33.6, s = 1.5, sample size is 18. Determine 95% confidence...

[t-interval] If sample mean = 33.6, s = 1.5, sample size is 18. Determine 95% confidence interval. Select the closest answer from below A. (32.85 , 34.35) B. (32.91 , 34.29) C. (33.02 , 34.18) D. (32.98 , 34.21)

Determine the sample size n needed to construct a 95?% confidence interval to estimate the population...

Determine the sample size n needed to construct a 95?% confidence interval to estimate the population proportion for the following sample proportions when the margin of error equals 55?%. a. p? = 0.50 b. p = 0.60 c. p = 0.70

Determine the sample size n needed to construct a 95% confidence interval to estimate the population...

Determine the sample size n needed to construct a 95% confidence interval to estimate the population mean for the following margins of error when sigma equals 67. a) 25 b) 40 c) 50

Determine the sample size n needed to construct a 95% confidence interval to estimate the population...

Determine the sample size n needed to construct a 95% confidence interval to estimate the population proportion for the following sample proportions when the margin of error equals 4%. a. p over bar equals 0.10 b. p over bar equals 0.20 c. p over bar equals 0.30

Match the terms with the following descriptions: population sample population size sample size population mean sample...

Match the terms with the following descriptions: population sample population size sample size population mean sample mean variance standard deviation alpha null hypothesis alternative hypothesis degrees of freedom hypothesized mean p-value t-statistic The set of data for ALL individuals or items of interest., e.g. everyone in the world, the entire of Texas, all of our customers, etc. __________ Data you take randomly from the population because it’s too costly or not feasible to measure the entire population. A subset of...

Subjects