Question

When asked whether marriage is becoming obsolete,742 out of 2089 randomly selected adults answering a particular survey said yes. We are testing the hypothesis that the population proportion that believes marriage is becoming obsolete is more than 34 % using a significance level of 0.05. One of the following figures is correct. Indicate which graph matches the alternative hypothesis,

p greater than 0.34

.

Report and interpret the correct p-value.

Choose the correct graph below.

A.

A graphing calculator output displays a coordinate system with horizontal axis from more than 3 ticks to the left of the vertical axis to more than 3 ticks to the right and a vertical axis from more than 1 tick below to 5 ticks above the horizontal axis. A Normal curve extends between the left and right edges of the graph with a peak 4 ticks high on the vertical axis at horizontal coordinate 0. Between the first and second tick marks to the right of the verical axis, a vertical line segment extends from the horizontal axis to the curve. The area under the curve to the left of the segment is shaded.

z equals

1.466

p equals

0.9287

B.

A graphing calculator output displays a coordinate system with horizontal axis from more than 3 ticks to the left of the vertical axis to more than 3 ticks to the right and a vertical axis from more than 1 tick below to 5 ticks above the horizontal axis. A Normal curve extends between the left and right edges of the graph with a peak 4 ticks high on the vertical axis at horizontal coordinate 0. Vertical line segments extend from the horizontal axis to the curve between the first and second tick marks to the left of the vertical axis and between the first and second tick marks to the right of the vertical axis. The areas under the curve to the left of the left segment and to the right of the right segment are shaded.

zquals

1.466

p equals

0.1426

C.

A graphing calculator output displays a coordinate system with horizontal axis from more than 3 ticks to the left of the vertical axis to more than 3 ticks to the right and a vertical axis from more than 1 tick below to 5 ticks above the horizontal axis. A Normal curve extends between the left and right edges of the graph with a peak 4 ticks high on the vertical axis at horizontal coordinate 0. Between the first and second tick marks to the right of the verical axis, a vertical line segment extends from the horizontal axis to the curve. The area under the curve to the right of the segment is shaded.

z equals

1.466

p equals

0.0713

Answer 1

When asked whether marriage is becoming obsolete,742 out of 2089 randomly selected adults answering a particular survey said yes. We are testing the hypothesis that the population proportion that believes marriage is becoming obsolete is more than 34 % using a significance level of 0.05. One of the following figures is correct. Indicate which graph matches the alternative hypothesis,

Here we have follwoing information:

Hypotheses are:

Standard deviation of the proportion is:

Test statistics will be:

Test is right tailed so p-value of the test is

p-value =P(z > 1.466) = 0.0713

Since p-value is greater than 0.05 so we fail to reject the null hypothesis.

Following curve shows the p-value: