Question

a)Sketch the distribution curve showing the area in the tails and the critical values.

b)Show any expressions that determine the confidence interval (such as margin of error) with the numbers in place and calculate the necessary value(s).

c)Write the confidence interval in the usual way (for example 4.34<p<5.68)

1)The number of non-native plants in a plot of 1 square meter is determined for 28 randomly-selected plots. The sample has a mean of 8.50 plants and a standard deviation of 0.72 plants.Obtain the confidence interval for the population mean, , using a confidence level of 90%.

Although the standard deviation is not known, if we assume that the standard deviation = 72.0 plants,how many plots should be sampled if we want to estimate the mean within 10.0 +- with a confidence level of 90%?

Answer 1

1)

Given

n = 28

s = 0.72

Confidence level = 90%

Since population standard deviation is unknown, we have to use t-distribution.

Degrees of freedom = n -1 = 28 -1 = 27

From the t-table,

Now

the 90% confidence interval for the population mean

  

( 8.27 , 8.73 )

Therefore, the 90% confidence interval for population mean is

Given

Standard deviation, = 72

Margin of error = 10

Confidence level = 90%

Since population standard deviation is known, we have to use z-distribution.

For 90% confience interval, the critical Z-value is 1.645

Now

Margin od error = critical value * standard error

The number of plots that should be sampled is 140.