Question

1.A local newspaper launched a website where they invited people to indicate their approval or disapproval of a new by-law. The resulting sample is likely

representative of the local population

biased

very accurate

unbiased

the best way to collect this kind of information

2.Consider the population of families with three children. If a family is selected at random from this population, and the genders of the three children are listed in order of age, e.g. (M, F, F), how many possible outcomes are there in the resulting sample space?

4

6

9

8

3.Suppose X is normally distributed with mean 4 and standard deviation 4. Find the probability that 3X exceeds 7.

.6615

.4555

.3011

.5497

.6012

4.Suppose the mean of a population distribution is μ. The average of a sample from the distribution of size n is x¯ and the sample standard deviation is S. Which quantity below has a t distribution?

μ−x¯S/nμ−x¯S/n

X¯−μσ/nX¯−μσ/n

X¯−μS/nX¯−μS/n

5.A contractor wishes to lower heating bills by using a special type of insulation in houses. The mean of the heating bill announced by the Energy Resource is 85. To determine if the special insulation will reduce heating costs, the contractor collects 20 heating bills from houses that already use the special type of insulation. The average of a heating bill for these 20 houses is 78. State the null and alternative hypotheses.

H₀: μμμμ=78 and H_A: μμμμ<85

H₀: μμμμ=85 and H_A: μμμμ <85

H₀:X¯X¯X¯X¯=78 and H_A: X¯X¯X¯X¯<85

H₀: μμμμ=78 and H_A: μμμμ>78

Answer 1

1) Biased

As it is given that the invitation was sent to indicate the approval or disapproval, then all the people who were invited need not necessarily fill up the details and hence the obtained sample would be biased.

2) 8

As the 3 gender of 3 children are ordered as per their age, the number of possible outcomes are as follows

MMM,MMF,MFM,FMM,FFM,FMF,MFF,FFF

Hence there can be 8 possible ways.

3) 0.6615

4) The options are not clearly readable but the answer is as follows

So this quantity t follows t distribution

5) Option 2

Vs

Thank you !!!