a-researcher-claims-that-the-mean-weight-of-apples-in-a-storage-bin-is-180180-gr

Question

A researcher claims that the mean weight of apples in a storage bin is $180$ grams. To test this claim, a quality control officer collects a random sample of $12$ apples, and records their weights (in grams) as:

$178 comma 182 comma 175 comma 180 comma 176 comma 179 comma 181 comma 183 comma 177 comma 179 comma 180 comma 178$

Assuming that the weights are normally distributed, and the sample standard deviation is approximately $2.38$ grams, determine whether there is enough evidence at the $0.05$ significance level to reject the researcher’s claim that the mean weight is $180$ grams.

Accepted Answer

Fail to reject $180$ ; there is not enough evidence to show the mean is different from $180 g$

Answer

Reject $180$ ; the mean is definitely greater than $180 g$

Answer

Reject $180$ ; there is strong evidence the mean is different from $180 g$

Answer

Fail to reject $180$ ; this proves the mean is exactly $180 g$