A farmer claims that the mean weight of the melons grown in his farm is at least $1.2$ kg. A rando

Question

A farmer claims that the mean weight of the melons grown in his farm is at least $1.2$ kg. A random sample of $10$ melons is chosen and the weight, $x$ kg, of each melon is recorded. The results are as follows: $1.037$ $0.914$ $1.019$ $1.234$ $1.110$ $1.417$ $1.008$ $0.846$ $1.105$ $1.331$ Another random sample of $40$ melons is weighed and the results are as follows: Another random sample of $40$ melons is weighed and the results are as follows: By combining the $2$ sets of data, find unbiased estimates of the population mean and population variance of the weight of a melon grown by this farmer.[2] The farmer decides to change the claim to “the mean weight of the melons grown in his farm is at least $m$ kg”. Based on the combined sample of size $50$, find the set of values of $m$ for which the farmer’s claim is not rejected at the $5\%$ significance level. [3]

Accepted Answer

(i) Unbiased estimate of population mean$=1.13518$; Unbiased estimate of population variance$=0.42001$ (ii) $0\le m<1.29$ ($3$ s.f.)

2015 AJC P2 Q10 [Modified]

2015 AJC P2 Q10 [Modified]