Question 55 – 2.5.3 Hypothesis test for a Normal mean (A-level only) - Questions

A chemical engineer is investigating whether a new catalyst increases the yield of a specific synthetic reaction. The yield, measured in grams per batch, is denoted by $y$ . A random sample of 80 batches produced without the catalyst (Group 1) and an independent random sample of 120 batches produced with the catalyst (Group 2) were recorded. The results are summarized in the table below:

Sample Group	Sample Size	$∑y\sum y$	$∑y2\sum y^2$	Unbiased estimate of mean	Unbiased estimate of variance
Without catalyst	80	6240	492000	$yˉ1\bar{y}_1$	$s_1^2$
With catalyst	120	—	—	81.5	380.4

Calculate the values of $yˉ1\bar{y}_1$ and $s_1^2$ .

Test, at the 1% level of significance, whether there is evidence that the mean yield is greater when the catalyst is used. State your hypotheses clearly.

Sample Group	Sample Size	$∑y\sum y$	$∑y2\sum y^2$	Unbiased estimate of mean	Unbiased estimate of variance
Without catalyst	80	6240	492000	$yˉ1\bar{y}_1$	$s_1^2$
With catalyst	120	—	—	81.5	380.4

Calculate the values of $yˉ1\bar{y}_1$ and $s_1^2$ .

Test, at the 1% level of significance, whether there is evidence that the mean yield is greater when the catalyst is used. State your hypotheses clearly.

2.5.3 Hypothesis test for a Normal mean (A-level only)

Question 11

2.5.3 Hypothesis test for a Normal mean (A-level only)

Question 11

2.5.3 Hypothesis test for a Normal mean (A-level only)

Question 11

2.5.3 Hypothesis test for a Normal mean (A-level only) Questions

2.5.3 Hypothesis test for a Normal mean (A-level only)

Question 11

2.5.3 Hypothesis test for a Normal mean (A-level only) Questions