Answer to Question #350338 in Statistics and Probability for Jhovan

Question

Activity 2: Maximum Error E

Activity 2: Maximum Error E

Assuming that the samples come from a normally distributed population, find

the maximum error E given the following:

Given

Solution and Answer

1.

n = 10, X= 28, s = 4.0,

90% confidence

2. n = 16, X= 50, s = 4.2,

95% confidence

3. n = 25, X= 92.8, s = 2.6,

99% confidence

Assuming that the samples come from a normally distributed population, find

the maximum error E given the following:

Given

Solution and Answer

1.

n = 10, X= 28, s = 4.0,

90% confidence

2. n = 16, X= 50, s = 4.2,

95% confidence

3. n = 25, X= 92.8, s = 2.6,

99% confidence

Answer 1

1.

A 90% confidence interval, $df=n-1=9$ degrees of freedom has a

t-score (a critical value) $t_c=1.833113.$

$$ME=t_c\times\dfrac{s}{\sqrt{n}}$$ $$=1.833113\times\dfrac{4.0}{\sqrt{10}}=2.3187$$

2.

A 95% confidence interval, $df=n-1=24$ degrees of freedom has a

t-score (a critical value) $t_c=1.833113.$

$$ME=t_c\times\dfrac{s}{\sqrt{n}}$$ $$=2.131449\times\dfrac{4.2}{\sqrt{16}}=2.2380$$

3.

A 99% confidence interval, $df=n-1=24$ degrees of freedom has a

t-score (a critical value) $t_c= 2.79694.$

$$ME=t_c\times\dfrac{s}{\sqrt{n}}$$ $$= 2.79694\times\dfrac{2.6}{\sqrt{25}}=1.4544$$