Question

A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 443 gram setting. It is believed that the machine is underfilling the bags. A 15 bag sample had a mean of 434 grams with a standard deviation of 17. A level of significance of 0.1 will be used. Assume the population distribution is approximately normal. Determine the decision rule for rejecting the null hypothesis. Round your answer to three decimal places.

Answer 1

Solution :

This is the left tailed test,  

The null and alternative hypothesis is ,

H₀ :   = 443

H_a : < 443

Test statistic = t =

= ( - ) / s / n

= (434 - 443 ) / 17 / 15

Test statistic = t = -2.050

degrees of freedom = n - 1 = 15 - 1 = 14

= 0.1

P(t > t) = 0.1

= 1 - P(t < t) = 0.1

= P(t < t) = 1 - 0.1

= P(t < t) = 0.9

= P(t < 1.345 ) = 0.9

t > 1.345

Fail to reject H₀ , because critical value > test statistic