Question

please solve and highlight answers

At Ajax Spring Water a half-liter bottle of soft drink is supposed to contain a mean of 533 ml. The filling process follows a normal distribution with a known process standard deviation of 7 ml (a) The normal distribution should be used for the sample mean because (You may select more than one answer. Click the box with a check mark for the correct answer and click to empty the box for the wrong answer.) the sample population has a large mean. 2 the population distribution is known to be normal. the population standard deviation is known. the standard deviation is very small. (b)Set up hypotheses and a two-tailed decision rule for the correct mean using the 5 percent level of significance. The hypothesis for a two-talled decision is a. Ho u +533. Hi =533. reject If z<-196 or z> 1.96 b. HON #533. Hi u = 533,reject if z> 1.96 or z<-1.96 C. Ho v = 533. Hy #533. reject if z> 1.96 or z<-1.96 d. Ha u=533. Hy #533. reject if z>-196 or 2 <1.96 OD (c)lf a sample of 16 bottles shows a mean fill of 530 ml. does this contradict the hypothesis that the true mean is 533 ml? No

yes

Answer 1

Solution:

Given:

At Ajax Spring Water , half-liter bottle of drink is supposed to contain a mean of 533 ml.
The filling process follows a Normal distribution with a known process standard deviation of 7 ml.

Part a)

The population distribution is known to be Normal
The population standard deviation is known

Part b)

two tailed test, with 5% level of significance.

Since this is two tailed test, we find probability =

a/2 = 0.05/2 = 0.025

Use excel command:

=NORM.S.INV( probability)

=NORM.S.INV(0.025)

=-1.96

Since this is two tailed test , rejection region is:

Reject H0 if z > +1.96 or z < -1.96

Thus correct option is:
Reject if z > 1.96 or z < -1.96

c) Ho: M = 533 vs H : #533

Part c)

Sample size = n = 16

Sample mean =

7=530

urlo

530 – 533 7/ 16

مس

3 1.75

2 = -1.71

Since z test statistic value is neither < -1.96 , nor > 1.96, we fail to reject null hypothesis.

Thus this sample does not contradict the hypothesis that the true mean is 533 ml.

Thus answer is : No