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A manufacturer of banana chips would like to know whether its bag filling machine works correctly...

A manufacturer of banana chips would like to know whether its bag filling machine works correctly at the 432 gram setting. It is believed that the machine is underfilling the bags. A 24 bag sample had a mean of 426 grams with a variance of 225. A level of significance of 0.01 will be used. Assume the population distribution is approximately normal. State the null and alternative hypotheses.

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Solution: Sample mean 426 Sample standard deviation S V225 Sample size n 24 Level of significance-α 0.01 Claimed population mean u 432 15 Null Hypothesis Alternate Hypothesis: HA:H < 432 Ho: μ 432 Degrees of Freedom - df-n -1 24 1 23 Test Statistic: 426-432 15 V24 t1.960 From t-distribution table; the area in lower tail to the left of (t =-1960) and for (df-23), is given by: 0.0311 Hence, p-value 0.0311 Since, p-value> a, we fail to reject the null hypothesis Conclusion At 1% level of significance, we do not have the sufficient evidence to conclude that the machine is under filling the bags

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