Question

A manufacturer of banana chips would like to know whether its bag filling machine works correctly at the 431 gram setting. It is believed that the machine is underfilling the bags. A 23 bag sample had a mean of 423 grams with a standard deviation of 14. Assume the population is normally distributed. A level of significance of 0.05 will be used. Find the P-value of the test statistic. You may write the P-value as a range using interval notation, or as a decimal value rounded to four decimal places.

Answer 1

Solution :

= 431

=423

=14

n = 23

Degree of freedom, n−1=23−1=22

In this question, we will use the 't distribution to test the null and the alternative hypothesis statements about the population mean at 0.05 level of significance. The t distribution is a sampling distribution based on (n-1) degree of freedom.

The null hypothesis is,

H0:μ≥431

The alternative hypothesis is,

H0:μ<431

Test statistic = z

= ( - ) / / n

= (423-431) / 14 / 23

= -2.74

P-value = 0.006

= 0.05  

P-value <

he result is significant at p < .05.

Reject the null hypothesis .

There is sufficient evidence to suggest that