I need asap pleaassee

A survey was conducted to determine the average age at which college seniors hope to retire in a simple random sample of 101 sen

tatyana61 [14]

Answer:

96% confidence interval for desired retirement age of all college students is [54.30 , 55.70].

Step-by-step explanation:

We are given that a survey was conducted to determine the average age at which college seniors hope to retire in a simple random sample of 101 seniors, 55 was the average desired retirement age, with a standard deviation of 3.4 years.

Firstly, the Pivotal quantity for 96% confidence interval for the population mean is given by;

P.Q. = $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

where, $\bar X$ = sample average desired retirement age = 55 years

$\sigma$ = sample standard deviation = 3.4 years

n = sample of seniors = 101

$\mu$ = true mean retirement age of all college students

Here for constructing 96% confidence interval we have used One-sample t test statistics as we don't know about population standard deviation.

So, 96% confidence interval for the population mean, $\mu$ is ;

P(-2.114 < $t_1_0_0$ < 2.114) = 0.96 {As the critical value of t at 100 degree

of freedom are -2.114 & 2.114 with P = 2%}

P(-2.114 < $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ < 2.114) = 0.96

P( $-2.114 \times {\frac{s}{\sqrt{n} } }$ < ${\bar X-\mu}$ < $2.114 \times {\frac{s}{\sqrt{n} } }$ ) = 0.96

P( $\bar X-2.114 \times {\frac{s}{\sqrt{n} } }$ < $\mu$ < $\bar X+2.114 \times {\frac{s}{\sqrt{n} } }$ ) = 0.96

96% confidence interval for $\mu$ = [ $\bar X-2.114 \times {\frac{s}{\sqrt{n} } }$ , $\bar X+2.114 \times {\frac{s}{\sqrt{n} } }$ ]

= [ $55-2.114 \times {\frac{3.4}{\sqrt{101} } }$ , $55+2.114 \times {\frac{3.4}{\sqrt{101} } }$ ]

= [54.30 , 55.70]

Therefore, 96% confidence interval for desired retirement age of all college students is [54.30 , 55.70].

7 0

2 years ago

Select the postulate that is illustrated for the real numbers 5+(-5)=0

ozzi

In this question , we have to find the postulate that is illustrated for the real numbers

$5+(-5) = 0$

The postulate is Additive inverse postulate which states that

$a+ (-a) =0$

Where a is the real number and -a is the opposite of a. It states that , if opposite of a number is added with the number, the result is 0 .

3 0

3 years ago

Read 2 more answers

Which equation is not equal to 6^3/6^6 ?: 1/6^2 6^-3 1/216 1/6^3

SCORPION-xisa [38]

The answer would be 60 because its multiplication all those numbers

4 0

2 years ago

Again asap and sorry for the mess…

skelet666 [1.2K]

Answer:

185 shrubs

Step-by-step explanation:

ratio plant : 1% = 5 : 1%

if the percent of shrubs in the garden is 37%, according to my ratio. every 1% is 5 plants, therefore, 37% = 37 x 5 = 185

6 0

1 year ago

In one month, Claudia rides her favorite bike trail 12 times. She travels a total distance of 1182 km. What is the length of Cla

kati45 [8]

The length of the trail is 98.5 KM, all you need to do is divide the total distance by the number of times she went on it.

4 0

2 years ago

Read 2 more answers