Question

A random sample of 1000 apples has mean weight of 187 gms and .D. 8 gms. Another random sample of 800 apples has mean weight of 188.4 gms and .D. of 10 gms. Test the hypothesis that the mean weights differ significantly at 1% level of significance.

Answer 1

Given: n1 = 1000; x̄1

=187gms, S1 = 8 gms

n2 = 800; x̄2 = 188gms,

S2 = 10 gms

H0 : means are same

(i.e., H0 : µ< sub.1 = µ2}

H, : means are not same.

( i.e., H, : µ1 ≠ µ2)

{Two tailed test}

The test statistics is –

At α = 5% the critical values are – K1

= – 1.96, K2 = 1.96.

Here Zeal = – 3.22 is out side of -K1 and K2

∴ H0 is rejected and H1 is accepted.

Conclusion: Mean weight of apples are same.