2.5 Statistical Hypothesis Testing

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Question 32

The temperature of water ( $w∘Cw^\circ\text{C}$ ) in a kettle $t\,$ minutes after it was boiled is recorded in the table below


$t$	1	3	6	9	11	15	20
$w$	92	76	65	50	46	33	25

The data is coded using the changes of variable $x = t$ and $y = \log_{10} w$

The regression line of $x\,$ on $y\,$ is found to be $y = 1.99 - 0.031 x$

Given that the data can be modelled by an equation in the form $w = ab^t$ where $a\,$ and $b\,$ are constants. Find the values of $a\,$ and $b\,$ to 3 significant figures.

[3]

Give an interpretation of the constant $a\,$ in this equation.

[1]

Explain why this model is not reliable for calculating the temperature after 1 hour.

[1]

2.5 Statistical Hypothesis Testing

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Question 32

The temperature of water ( $w∘Cw^\circ\text{C}$ ) in a kettle $t\,$ minutes after it was boiled is recorded in the table below


$t$	1	3	6	9	11	15	20
$w$	92	76	65	50	46	33	25

The data is coded using the changes of variable $x = t$ and $y = \log_{10} w$

The regression line of $x\,$ on $y\,$ is found to be $y = 1.99 - 0.031 x$

Given that the data can be modelled by an equation in the form $w = ab^t$ where $a\,$ and $b\,$ are constants. Find the values of $a\,$ and $b\,$ to 3 significant figures.

[3]

Give an interpretation of the constant $a\,$ in this equation.

[1]

Explain why this model is not reliable for calculating the temperature after 1 hour.

[1]

2.5 Statistical Hypothesis Testing

Question 32

Markscheme

2.5 Statistical Hypothesis Testing

Question 32

Markscheme

2.5 Statistical Hypothesis Testing

Question 32

2.5 Statistical Hypothesis Testing Questions

2.5 Statistical Hypothesis Testing

Question 32

2.5 Statistical Hypothesis Testing Questions