According to a 2011 nationwide telephone survey of American adults. 70% of adult

Question

According to a 2011 nationwide telephone survey of American adults. 70% of adults said that college education has become too expensive for most people and they cannot afford it. Suppose that this result is true for the 2011 population of American adults. In a more recent poll of 2000 American adults, 1350 said that college education had become too expensive for most people and they cannot afford it. Using a 1% significance level, perform a lest of hypothesis to determine whether the current percentage of American adults who will say that college education has become too expensive for most people and they cannot afford it is lower than 70%. Use both the p-value and critical-value approaches.

Explanation / Answer

Here we have to test the hypothesis that,

H0 : p = 70% = 0.70 Vs H1 : p < 70% = 0.70

where p is the population proportion of adults say that college education has become too expensive for most people and they cannot afford it.

Assume alpha = significance level = 1% = 0.01

Given that n = number of American adults = 2000

x = number of adults said that  college education has become too expensive for most people and they cannot afford it = 1350

sample proportion (p^) = 1350 / 2000 = 0.675

This testing we can done using TI-83 calculator.

steps :

STAT --> TESTS --> 5:1-PropZTest --> ENTER --> Input p0, x, n --> Prop : < p0 --> ENTER --> Calculate --> ENTER

Output is,

Test statistic Z = -2.43975

P-value = 0.00735

P-value < alpha

Critical value we can find by using EXCEL.

syntax is,

=NORMSDIST(probability)

where probability = alpha

critical value = -2.33

Take absolute value of test statistic and critical value.

Test statistic > critical value

Reject H0 at 1% level of significance.

Conclusion : The current percentage of American adults who will say that college education has become too expensive for most people and they cannot afford it is lower than 70%.

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