Question

The coffee and soup machine at the local subway station is supposed to fill cups with 6 ounces of soup. Ten cups of soup are bought with results of a mean of 5.93 ounces and a standard deviation of 0.13 ounces. How large a sample of soups would we need to be 95 percent confident that the sample mean is within 0.03 ounces of the population mean?

Answer 1

Answer:

sample size is 73

Step-by-step explanation:

Given data

mean = 5.93

standard deviation = 0.13

confident = 95%

sample mean = 0.03

top find out

sample of soups

solution

we know Z critical value is  1.96 with the help of Z table when a = 0.05 ( 95 % confident)  and sample mean is 0.03

so sample = (( Z × standard deviation  ) / sample mean)^2    ...................1

so now put all value  Z ,  standard deviation and sample mean in equation 1

sample = (( Z × standard deviation  ) / sample mean)^2

sample = (( 1.96 ×  0.13  ) / 0.03)^2

sample = 72.137

so sample size is 73

Answer 2

Answer:

Required sample size = 73

Explanation:

Let $\mu$ be the population mean for the amount of soup /coffee filled in cups.

Further explanation:

Given : The coffee and soup machine at the local subway station is supposed to fill cups with 6 ounces of soup.

Ten cups of soup are bought with results of a mean of 5.93 ounces and a standard deviation of 0.13 ounces.  

i.e. For sample size of n =10 ,  

Sample mean : $\overline{x}=5.93\text{ ounces}$

Sample standard deviation : $s=0.13 \text{ ounces}$

Since, the sample standard deviation(s) is the best estimate for population standard deviation $(\sigma)$.

Thus , the estimated population standard deviation $(\sigma)=0.13$.

Margin of error (distance between the confidence interval limits and the mean -value) :E=0.003 ounces

Critical z-value for 95% confidence interval : $z_{\alpha/2}=1.96$ (Using z-table calculator)

The formula use to find the minimum required sample size :-

$n=(\dfrac{z_{\alpha/2}\cdot \sigma}{E})^2$

$n=(\dfrac{1.96\times 0.13}{0.03})^2=72.1367111111\approx73$

Hence, the required minimum sample size : n= 73

Learn More :

https://brainly.com/question/9760478 (Answered by MsEHoltBrainly Teachers)

https://brainly.com/question/13710349 (Answered by Jeanashupp)

Key words :

Sample size , z-table , Confidence level , Margin of error .