<p style="margin-bottom: 1.25rem">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:</p>
<div class="content-block content-block--table"><div class="table-container"><table style="table-layout: fixed; width: 450px;"><colgroup><col style="width: 90px;"><col style="width: 90px;"><col style="width: 90px;"><col style="width: 90px;"><col style="width: 90px;"></colgroup><thead><tr style="height: 23px;"><th style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p>$1.037$</p></th><th style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p>$0.914$</p></th><th style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p>$1.019$</p></th><th style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p>$1.234$</p></th><th style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p>$1.110$</p></th></tr></thead><tbody><tr style="height: 23px;"><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p>$1.417$</p></td><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p>$1.008$</p></td><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p>$0.846$</p></td><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p>$1.105$</p></td><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p>$1.331$</p></td></tr></tbody></table></div></div>
<p>Another random sample of $40$ melons is weighed and the results are as follows:</p>
<p style="text-align: center">Another random sample of $40$ melons is weighed and the results are as follows:</p>
<ol class="i-list"><li><div class="list-item-paragraph">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.<span class="inline-marks">[2]</span></div></li><li><div class="list-item-paragraph">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.	<span class="inline-marks">[3]</span></div></li></ol>

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:

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.

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.	

Hypothesis Testing

International Baccalaureate Higher Level Mathematics

2015 AJC P2 Q10 [Modified]

2015 AJC P2 Q10 [Modified]