Question

Nestor Milk Powder is sold in packets with an advertised mean weight of 1.5kgs. The standard deviation is known to be 184 grams. A consumer group wishes to check the accuracy of the advertised mean and takes a sample of 52 packets finding an average weight of 1.49kgs. What is the set of hypotheses that should be used to test the accuracy of advertised weight?

(a) oH:μ= 1.49; 1H: μ≠1.49
(b) oH:μ= 1.5; 1H: μ< 1.5
(c) oH: μ= 1.5; 1H: μ≠1.5
(d) oH: x = 1.5; 1H: x < 1.5

Answer 1

Answer: c)
`H_0:\mu= 1.5\\\\H_a:\mu \\eq1.5`

Explanation:

Given: Nestor Milk Powder is sold in packets with an advertised mean weight of 1.5 kgs.

i.e.
`\mu= 1.5`

A consumer group wishes to check the accuracy of the advertised mean and takes a sample of 52 packets finding an average weight of 1.49 kgs.

So 1.49 is sample mean but hypothesis is the statement about the parameter which is
`\mu`.

i.e. he wanted to check whether
`\mu= 1.5` or
`\mu \\eq1.5`

Since null hypothesis
`(H_0)` contains equality and alternative hypothesis
`(H_a)` is against it.

Therefore, the set of hypotheses that should be used to test the accuracy of advertised weight would be :

`H_0:\mu= 1.5\\\\H_a:\mu \\eq1.5`

Hence, the correct answer is option c) oH: μ= 1.5; 1H: μ≠1.5