2.5 O: Statistical hypothesis testing

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Question 86

An electrical engineer is comparing the charging times of heavy-duty capacitors from two different manufacturers, Manufacturer P and Manufacturer Q. Random samples of 75 capacitors from Manufacturer P and 80 capacitors from Manufacturer Q are tested, and the charging time, $t$ minutes, of each capacitor is recorded.

The table below summarizes the data:

Manufacturer	Sample size ( $n$ )	Sum of $t$ ( $∑t\sum t$ )	Sum of $t^2$ ( $∑t2\sum t^2$ )	Unbiased estimate of the mean	Unbiased estimate of the variance
Manufacturer P	75	1860	46246.4	24.8	1.6
Manufacturer Q	80	2040	52494	$m$	$v$

Calculate the value of $m$ and the value of $v$ .

[3]

The engineer believes that the mean charging time of capacitors from Manufacturer P is shorter than the mean charging time of capacitors from Manufacturer Q.

Stating your hypotheses clearly, carry out a suitable test to assess the engineer's belief. Use a 5% level of significance and state your critical value.

[6]

Explain how you have used the Central Limit Theorem in your answer to part (b).

[2]

2.5 O: Statistical hypothesis testing

Question 86

The table below summarizes the data:

Manufacturer	Sample size ( $n$ )	Sum of $t$ ( $∑t\sum t$ )	Sum of $t^2$ ( $∑t2\sum t^2$ )	Unbiased estimate of the mean	Unbiased estimate of the variance
Manufacturer P	75	1860	46246.4	24.8	1.6
Manufacturer Q	80	2040	52494	$m$	$v$

Calculate the value of $m$ and the value of $v$ .

[3]

The engineer believes that the mean charging time of capacitors from Manufacturer P is shorter than the mean charging time of capacitors from Manufacturer Q.

Stating your hypotheses clearly, carry out a suitable test to assess the engineer's belief. Use a 5% level of significance and state your critical value.

[6]

Explain how you have used the Central Limit Theorem in your answer to part (b).

[2]

2.5 O: Statistical hypothesis testing

Question 86

Markscheme

2.5 O: Statistical hypothesis testing

Question 86

Markscheme

2.5 O: Statistical hypothesis testing

Question 86

2.5 O: Statistical hypothesis testing Questions

2.5 O: Statistical hypothesis testing

Question 86

2.5 O: Statistical hypothesis testing Questions