Question

When choosing an item from a group, researchers have shown that an important factor influencing choice is the item's location. This occurs in varied situations such as shelf positions when shopping, filling out a questionnaire, and even when choosing a preferred candidate during a presidential debate. In this experiment, five identical pairs of white socks were displayed by attaching them vertically to a blue background that was then mounted on an easel for viewing. One hundred participants from the University of Chester were used as subjects and asked to choose their preferred pairs of socks. In choice situations of this type, subjects often exhibit the "center stage effect," which is a tendency to choose the item in the center. In this experiment, 34 subjects chose the pair of socks in the center. Are these data evidence of the "center stage effect"?

STATE: Are the students choosing pairs of socks randomly? If the students were choosing socks at random, what would be the chance, ?0, of a pair being selected? (Enter your answer rounded to one decimal place.)

?0=

PLAN: Let ? be the proportion of times the center sock is chosen. What is the correct pair of hypotheses we are to test?

None of the options are correct.

?0:?=?0 versus ??:?≠?0

?0:?=?0 versus ??:?>?0

?0:?=?0 versus ??:?<?0

SOLVE: We are able to utilize the ? statistic to test our hypotheses. Why? Select the correct response.

There are strictly less than 10 successes.

There are at least 10 successes.

None of the options are correct.

Both the samples that are successes and failures are over 10.

Select the correct ? statistic.

?=−3.6

?=5.12

?=−0.024

?=3.5

CONCLUDE: Select the correct conclusion about the proportion of times the center pair of socks are selected.

There is weak evidence that the proportion of times the center sock is chosen more often than all the others.

We have insufficient evidence to make any conclusion because the sample of students examined was too small.

There is no evidence that the proportion of times the center sock is chosen more often than all the others.

There is strong evidence that the proportion of times the center sock is chosen more often than all the others.

Answer 1

1) The correct hypothesis is :
H0 : p = p0 vs Ha : p ≠ p0

2) To test the Z statistics, the major condition to be met are :
Both the samples that are successes and failures are over 10.

3) The Z-statistic is :
Z stat =
where is the estimated value and is :   = 34/100 = 0.34
P is the hypothetical value which is 1/5 i.e 0.20
And =   = = 0.04

Thus,  Z stat =   = 3.5

4) Since value is unknown, we assume it to be 0.05.
Thus from Z tables, Z () = Z (0.05) = 1.6449
Since Z stat > Z (0.05), we reject Ho at 5% l.o.s. and thus conclude that there is strong evidence that the proportion of times the center sock is chosen more often than all the others.

Hope this answers your query!