Question

Workers at a certain soda drink factory collected data on the volumes (in ounces) of a simple random sample of 15 cans of the soda drink. Those volumes have a mean of 12.19 oz and a standard deviation of 0.11 oz, and they appear to be from a normally distributed population. If the workers want the filling process to work so that almost all cans have volumes between 12.01 oz and 12.65 oz, the range rule of thumb can be used to estimate that the standard deviation should be less than 0.16 oz. Use the sample data to test the claim that the population of volumes has a standard deviation less than 0.16 oz. Use a 0.01 significance level. Complete parts (a) through (d) below. a. Identify the null and alternative hypotheses. Choose the correct answer below. O A. Ho: 6 = 0.16 oz H:0*0.16 oz 0 C. Họ: 0 = 0.16 oz OB. Ho: 02 0.16 oz H: 0<0.16 oz OD. Ho: 0>0.16 oz

B- Compute the Test statistic

x²=

C- Find the P-Value

Answer 1

Part a)

To Test :-

ОВ. На: 020.16 оz Ho<0.16 az

S² = 0.0121
α = 0.01
n = 15

Part b)
Test Statistic :-
$\chi ^2 = ( (n-1) S^2) / \sigma^2$
χ² = ( ( 15-1 ) * 0.0121 ) / 0.0256
χ² = 6.6172

Test Criteria :-
Reject null hypothesis if $\chi ^2 < \chi_{1 - \alpha, n - 1}^{2}$
χ² (1 - 0.01,15 - 1) = 4.66
$\chi ^2 > \chi_{1 - 0.01,15 - 1}^{2}$ = 6.6172 > 4.66 , hence we fail to reject the null hypothesis
Conclusion :- We Fail to Reject H0

Part c)
Decision based on P value
P value = P ( χ² > 6.6172 ) = 0.0515
Reject null hypothesis if P value < α = 0.01
Since P value = 0.0515 > 0.01, hence we fail to reject the null hypothesis
Conclusion :- We Fail to Reject H0

Part d)

Ho because the P-value is the level of significance. There is evidence to conclude that the population standard deviation of can volumes is less than 0.16 oz.

Fail to reject H0, P value is greater than α = 0.01, insufficient evidence to support the claim that population volume has standard deviation less than 0.16 oz.