Final answer:
To determine if the proportion of smartphone owners at the university is lower than 80%, we set up a null hypothesis (H₀: p = 0.80) and an alternative hypothesis (Ha: p < 0.80). The P-value calculated from a hypothesis test using StatCrunch tells us whether the null hypothesis can be rejected at a 5% significance level.
Step-by-step explanation:
Hypotheses:
Symbolic Form:
H₀: p = 0.80
Ha: p < 0.80
In Words:
The null hypothesis H₀ states that the proportion (p) of smartphone owners at the university is 80% (the same as the national average), whereas the alternative hypothesis Ha claims that the proportion (p) of smartphone owners is lower than 80%.
Normality Conditions:
For the normal model to apply, we require the sample size (n) to be such that np and n(1 - p) are both greater than 5. This condition must be checked with actual sample data before proceeding to the hypothesis test.
Conducting the Hypothesis Test:
StatCrunch: Instructions provided in the question would need to be followed to use StatCrunch for performing the hypothesis test. StatCrunch output would be inserted if the actual data were provided.
P-value Interpretation:
The P-value represents the probability of observing data as extreme as the sample data, assuming the null hypothesis is true. A low P-value (<0.05) suggests that the evidence is strong enough to reject the null hypothesis in favor of the alternative hypothesis.
Conclusion:
Given a significance level of 5%, if the P-value is less than 0.05, we reject the null hypothesis and conclude that the proportion of smartphone owners at the university is statistically significantly lower than 80%. Without actual P-value data, we cannot make a definitive conclusion.