A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 405 gram setting. It is believed that the machine is underfilling the bags. A 22 bag sample had a mean of 396 grams with a variance of 441. A level of significance of 0.1 will be used. Assume the population distribution is approximately normal. Required:
State the null and alternative hypotheses.

We reject H₀

Step-by-step explanation:

Normal Distribution with  n  = 22   ( sample size)

n<30 we need to use a t-student distribution

Sample mean  μ =   396        

Population mean  ( required mean )  μ₀  = 405

Sample variance is  441 then sample standard deviation s = √441

s  =  21

Hypothesis Test

Null Hypothesis                                          H₀         μ   =   μ₀

Alternative Hypothesis                               Hₐ       μ   <   μ₀

Significance level   α = 0,1    

The test is a one-tail test to the left

From t-student table we find for  t(c)

degree of fredom     df  = 22 -1       df  =  21

and  α = 0,1           t(c)  =  - 1,3232

To compute t(s)

t(s)  =  ( μ  -  μ₀ ) / s /√n

t(s)  =  ( 396  - 405 )*√n / 21

t(s)  =  - 9 *4,69 /21

t(s)  =  -  2,01

Comparing

t(s) and  t(c)          - 2,01     and   - 1,3232

|t(s)| > |t(c)|   then   t(s) is in the rejection region we must reject H₀

-7

step-by-step explanation:

x^2 + 18x + 74 = (x + 9)^2 - 81 + 74

= (x + 9)^2 - 7.

so q = -7.