Answer:
(a) Population mean = 314.5mg
(b) Margin of error = 21.281mg
(c) No, 350mg is not a plausible value
The new brand of hot dog has a lower sodium content on average than the leading brand
(d) Yes
Step-by-step explanation:
(a) Population mean = (370+326+322+297+326+289+293+264+327+331)/10 = 3145/10 = 314.5mg
(b) Margin of error = t×sd/√n
sd = 29.73, n = 10, degree of freedom = n-1 = 10-1 = 9
Assuming 95% confidence level
t-value corresponding to 9 degrees of freedom and 95% confidence level is 2.262
Margin of error = 2.262×29.73/√10 = 21.281mg
(c) No
Lower limit of new brand = 314.5 - 21.281 = 293.219mg
Upper limit = 314.5 + 21.281 = 335.781mg
The range of sodium content for the new brand of hot dog is between 293.219mg and 335.781mg which is lower than the leading brand (350mg)
(d) Margin of error = t×sd/√n
From the formula above, margin of error varies inversely as the square root of sample size
The smaller the sample size (n = 10) the larger the margin of error and the less accurate is the population mean
The larger the sample size (n = 40) the smaller the margin of error and the more accurate is the population mean
