Question

A researcher for Agri-Giant Corporation wants to study how many pounds of tomatoes are typically picked by a manual labourer in an 8-hour day. The Corporation will consider using picking machines if the labourers cannot pick at least 240 pounds, on average. The researcher randomly sampled 100 farm labourers, found out how many pounds of tomatoes each picked and calculated the sample mean and standard deviation.

Part a) Which of the following is/are parameter(s) of interest with respect to the new investigation here? (Select all that apply)

A. 240 pounds
B. 8 hours
C. The average number of pounds of tomatoes picked by the 100 manual labourers.
D. 100
E. The total number of pounds of tomatoes each labourer picks in an 8 hour shift.
F. The variance of the weights of tomatoes typically picked by a manual labourer in an 8-hour day.
G. The average number of pounds of tomatoes typically picked by a manual labourer in an 8-hour shift.
H. None of the above

Part b) In testing a hypothesis about a parameter of interest, what would your null hypothesis be?
The mean number of pounds of tomatoes typically picked by a manual labourer in an 8-hour shift is 240 pounds.
The mean number of pounds of tomatoes typically picked by a manual labourer in an 8-hour shift is greater than 240 pounds.
The mean number of pounds of tomatoes typically picked by a manual labourer in an 8-hour shift is less than 240 pounds.
The total number of pounds of tomatoes typically picked by a manual labourer in an 8-hour shift is 240 pounds.
The total number of pounds of tomatoes typically picked by a manuallabourer in an 8-hour shift is greater than 240 pounds.
The total number of pounds of tomatoes typically picked by a manual labourer in an 8-hour shift is less than 240 pounds.
The total number of pounds of tomatoes typically picked by a manual labourer in an 8-hour shift is different from 240 pounds.

Part c) You would take the alternative hypothesis to be:
one-sided, left-tailed
two-sided.
one-sided, right-tailed.
it does not matter whether we take a one-sided or two-sided alternative.

Part d) Suppose that, based on data collected, you reject the null hypothesis. Which of the following could you conclude?
There is sufficient evidence to suggest the mean number of pounds of tomatoes typically picked by a manual labourer in an 8-hour shift is less than 240 pounds.
There is sufficient evidence to suggest the mean number of pounds of tomatoes typically picked by a manual labourer in an 8-hour shift is 240 pounds.
There is sufficient evidence to suggest the mean number of pounds of tomatoes typically picked by a manual labourer in an 8-hour shift is greater than 240 pounds.
There is insufficient evidence to suggest the total number of pounds of tomatoes typically picked by a manual labourer in an 8-hour shift is 240 pounds.
There is insufficient evidence to suggest the total number of pounds of tomatoes typically picked by a manual labourer in an 8-hour shift is greater than 240 pounds.
There is insufficient evidence to suggest the total number of pounds of tomatoes typically picked by a manual labourer in an 8-hour shift is less than 240 pounds.

Part e) Suppose that, based on data collected, you decide that the mean number of pounds of tomatoes typically picked by a manual labourer in an 8-hour shift is less than 240 pounds.
it is possible that you are making a Type I error.
it is possible that you are making a Type II error.
it is certainly correct that the mean number of pounds of tomatoes typically picked by a manual labourer in an 8-hour shift is less than 240 pounds.
it is certainly incorrect that the mean number of pounds of tomatoes typically picked by a manual labourer in an 8-hour shift is less than 240 pounds.
there must have been a problem with the way the sample was obtained.

Part f) Suppose that, based on the data collected, you obtain a ?P-value of 0.02. This means:
the sample of labourers picked relatively less, if indeed the true mean number of pounds of tomatoes typically picked by a manual labourer in an 8-hour shift is 240 pounds.
there is a 2% chance that the mean number of pounds of tomatoes typically picked by a manual labourer in an 8-hour shift is less than 240 pounds.
there is a 2% chance that the mean number of pounds of tomatoes typically picked by a manual labourer in an 8-hour shift is greater than 240 pounds.
the probability of the mean number of pounds of tomatoes typically picked by a manual labourer in an 8-hour shift being 240 pounds or more is 0.02, if indeed the true mean number of pounds of tomatoes typically picked is 240 pounds
the probability of the mean number of pounds of tomatoes typically picked by a manual labourer in an 8-hour shift being 240 pounds or less is 0.02, if indeed the true mean number of pounds of tomatoes typically picked is 240 pounds
the sample of labourers picked relatively more, if indeed the true mean number of pounds of tomatoes typically picked by a manual labourer in an 8-hour shift is 240 pounds.

Part g) Based on the ?P-value that was obtained, you would (Select all that apply):

A. reject the null hypothesis at ?=0.1α=0.1 level of significance
B. fail to reject the null hypothesis at all.
C. believe the null hypothesis is true.
D. reject the null hypothesis at ?=0.05α=0.05 level of significance
E. neither reject nor accept the null hypothesis.
F. None of the above

Answer 1

Part a) Select all that apply:

A. 240 pounds
D. 100
F. The variance of the weights of tomatoes typically picked by a manual labourer in an 8-hour day.

Part b) The mean number of pounds of tomatoes typically picked by a manual labourer in an 8-hour shift is 240 pounds.

Part c) You would take the alternative hypothesis to be: one-sided, left-tailed

Part d) There is sufficient evidence to suggest the mean number of pounds of tomatoes typically picked by a manual labourer in an 8-hour shift is less than 240 pounds.

Part e) it is certainly correct that the mean number of pounds of tomatoes typically picked by a manual labourer in an 8-hour shift is less than 240 pounds.

Part f) the probability of the mean number of pounds of tomatoes typically picked by a manual labourer in an 8-hour shift being 240 pounds or more is 0.02, if indeed the true mean number of pounds of tomatoes typically picked is 240 pounds

Part g) D. reject the null hypothesis at =0.05 level of significance