Question

Use the following information to answer the following two questions. Many studies have investigated the question of whether people tend to think of an odd number when they are asked to think of a single-digit number (0 through 9). Combining results from several studies, Kubovy and Psotka (1976) used a sample size of 1,770 people, of whom 741 thought of an even number and 1,029 thought of an odd number. Consider investigating whether these data provide strong evidence that people have a tendency to think of an odd number rather than an even number in this situation.

a. Check whether a theory-based approach is appropriate for these data and hypotheses.

b. Calculate the standardized value of the statistic.

c. Determine an approximate p-value.

d. Summarize your conclusion.

Answer 1

Here, we have given that,

n1=Total Sample Size of people used by Kubovy and Psotka=1770 people

X1=Numbe of person thought of an even number=741

X2=Numbe of person thought of an odd number=1029

Now we estimate the proportion and as follows,

=1st sample proportion =

= 2nd sample proportion =

(A)

Here, the response from the both group who though even number and who tought odd number is binomial which is binary in nature and both groups is having independent subjects.

i.e. Here, we are using Test for two proportions (i.e. two sample proportion test).

(B)

Claim: To check whether there is difference in the proportion of people have a tendency to think of an odd number rather than an even number in this situation

The null and alternative hypotheses is as follows,

v/s

Now, we can find the standardized test statistics,

Z-statistics=

=

=

= -9.81

(C)

Now, we can find the p-value

= level of significance= 0.05

this is two tailed test

Pvalue = 2*P( Z< z) as this is two tailed test.

              = 2* P (Z < -9.81)

              = 2 * (0.0000)

              =0.000

Decision:

Here P-value < 0.05

we can reject the Ho null hypothesis.

(D)

Conclusion:

We can reject the Ho null hypothesis, We can conclude that there is sufficient evidence to support the claim there is difference in the proportion of people have a tendency to think of an odd number rather than an even number in this situation