Question

Accuracy of a laboratory scale. To assess the accuracy of a laboratory scale, a standard weight that is known to weigh 1 gram is repeatedly weighed 4 times. The resulting measurements (in grams) are: 0.95, 1.02, 1.01, 0.98. Assume that the scale weights when the true weight is 1 gram are normally distributed with sample standard deviation 0.03. At the 5% significance level, do these data provide evidence that the scale is accurate? Do the five steps to hypothesis testing to perform a critical value t-test.

Answer 1

given data and some calculation:-

sample size (n) = 4

sample sd (s) = 0.03

level of significance () = 0.05

here, as the sample size n) is small < 30 and sample sd (s) is known we will do 1 sample t test for mean.

hypothesis:-

where, is the population mean weight.

test statistic be:-

degrees of freedom =(n-1) = (4-1) = 3

t critical value for alpha=0.05,df =3,both tailed test be:-

[ from t distribution table ]

rejection rule:-

reject the null hypothesis if,

decision:-

so, we fail to reject the null hypothesis.

conclusion:-

there is sufficient evidence to say that these data provide evidence that the scale is accurate at 0.05 level of significance.

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