Question

A random sample of 8 envelopes are taken from a letter box of a post office and their weights in grams are found to be 12.1, 11.9, 12.4, 12.3, 11.9, 12.1, 12.4, 12.1. Does this sample indicate an average weight of the envelopes received at that post office is less than 12.35 gms at 1% level of significance.

Answer 1

Given: n=8, µ = 12.35, a= 1%

Here n is small use t-test (i.e., n < 30)

H0 : Average weight of the envelops is less than 12.35 gms.

i.e., H0 : µ = 12.35 gms.

H1 : Average weight of the envelope is less than 12.53 gms. i.e.,

H1 : (µ< 12.35 gms {left Tailed test}

Here, = Sample .D.

X̄ = Sample mean.

Let X be the weight in gms

∴ tcal = -2.83

For (n – 1) = (8 – 1) = 7. d.f the lower left tail crtical value, (from t-table) at 5% level of significance is -k1 =-1.90

Here tcal = -2.83 is in rejection region (tcal < ttab)

∴ H0 is rejected and H1 is accepted.

Conclusion : Average weight of envelops is less than 12.35 gms.