Question

A random sample of 40 bags of flour is weighed. It is found that the sample mean is 453.08 grams. All weights of the bags of flour have a population standard deviation of 5.42 grams. What is the lower limit of an 80% confidence interval for the population mean weight?

Select one:

A. No solution

B. 451.983 grams

C. 452.360 grams

D. 452.405 grams

After interviewing a sample of 100 residents of New Taipei City, you find that the mean AGE of the sample respondents is 35 years with a standard deviation of 5.0, and that AGE seems fairly normally distributed. However, you are told that the average age of New Taipei City is less than 37 years ten years ago. Based on your sample data, you need to test whether the true average age of all New Taipei City residents is still less than 37 years now. What are the most appropriate null and alternative hypotheses for this test?

Select one:

A. None of the other choices.

B. H₀: µ ≥ 37    versus    H₁: µ < 37   

C. H₀: µ = 37    versus    H₁: µ ≠ 37

D. H₀: µ < 37    versus    H₁: µ ≥ 37

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 453.08

Population standard deviation =    = 5.42

Sample size = n = 40

At 80% confidence level

= 1 - 80%  

= 1 - 0.80 = 0.2

/2 = 0.1

Z/2 = Z0.1 = 1.28

Margin of error = E = Z/2 * ( /n)

= 1.28 * ( 5.42 /  40)

= 1.097

At 80% confidence interval estimate of the population mean is,

- E

435.08 - 1.097

( 451.983 )

At 80% confidence interval estimate of the population mean is,( 451.983 )

Correct option : - ( B) 451.983 grams

( B )

The null and alternative hypothesis is ,

H0 :   37

H1 : < 37

This is the left tailed test .