Every clinical thermometer is classified into one of the four catergor

Question

Every clinical thermometer is classified into one of the four catergories A, B, C and D on the basis of inspection and test. From the past experience it is known that thermometers produced by a certain manufacturer are distributed among the four categories in the following proportions:

Category:	A	B	C	D
Proportion:	0.87	0.009	0.003	0.01

A new lot of 1336 thermometers is submitted by the manufacture for inspection and test and the following distribution of categories obtained:

Category:	A	B	C	D
No. of thermometers Reported:	1188	91	47	10

At 5% level of significance test whether this new lot of thermometers differ from the previous experience.

12 Mar 2024

Answer :

Word Count : 332

This problem requires performing a chi-square goodness-of-fit test to determine whether the observed distribution of thermometer categories differs significantly from the expected distribution based on past experience. --- ### Step 1: Define Hypotheses - Null Hypothesis (\(H_0\)): The new lot follows the same distribution as the past experience. - Alternative Hypothesis (\(H_1\)): The new lot follows a different distribution. --- ### Step 2: Calculate Expected Frequencies We calculate the expected number of thermometers in each category using: \[ E_i = p_i \times N ___ ___ ____ ____ _______ __________ _______ _________ ____ ________.
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Class interval	Frequency
0 – 10	5
10 – 20	10
20 – 30	14
30 – 40	15
40 – 50	6

$x\rightarrow$	$y\downarrow$	0	1	2
0		$\frac{1}{12}$	$\frac{1}{6}$	$\frac{1}{24}$
1		$\frac{1}{4}$	$\frac{1}{4}$	$\frac{1}{40}$
2		$\frac{1}{8}$	$\frac{1}{20}$	__
3		$\frac{1}{120}$	__	$\frac{1}{120}$