A manufacturer of banana chips would like to know whether its bag filling machine works correctly at the 434 gram setting. It is believed that the machine is underfilling or overfilling the bags. A 24 bag sample had a mean of 425 grams with a standard deviation of 16. Assume the population is normally distributed. A level of significance of 0.02 will be used. Specify the type of hypothesis test.
this is t test for a single population mean with unknown standard deviation
the test is two tailed
| null hypothesis:Ho μ | = | 434 | ||
| Alternate Hypothesis:Ha μ | ≠ | 434 | ||
| for 0.02 level with two tail test , critical z= | 2.33 | (from excel:normsinv(0.01) | ||
| Decision rule:reject Ho if absolute test stat|z|>2.33 | ||||
| population mean μ= | 434 | |
| sample mean 'x̄= | 425.000 | |
| sample size n= | 24 | |
| std deviation σ= | 16.000 | |
| std error ='σx=σ/√n=16/√24= | 3.2660 | |
| z statistic= ='(x̄-μ)/σx=(425-434)/3.266= | -2.76 | |
| since test statistic falls in rejection region we reject null hypothesis |
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