In: Math
Do you typically stop or speed up at a yellow traffic light?
Ho: proportion who speed up = 0.70 Ha: proportion who speed up ≠ 0.70
Average: .4375 Standard Deviation: .4961
The sample size is 32 and our focus is who does speed up at the yellow light.
How many speeding tickets have you had in your life?
Ho: average tickets = 5 Ha: average tickets ≠ 5
Average: 7.03 Standard Deviation: 10.00
Test the hypotheses and include a full calculation of the test statistic, p-value, and state the full conclusion in words for both problems. Show all work.
1)
Let the proportion, = sample proportion of those who does speed up at the yellow light.
To test whether there is significant difference in results from survey, the z test for the one proportion is used since the sample data values satisfy the normality condition
The null and alternative hypotheses are defined as,
Let the significance level of the test is
The z-statistic is obtained using the formula,
The p-value is obtained from z-distribution table for z = -3.2404
Since the P-value is 0.0012<0.05 at 5% significant level, the null hypothesis is rejected hence we can conclude that there is significant difference in sample and hypothesized proportion between those who does speed up at the yellow light.
2)
Since we are comparing one sample mean with the population and the population standard deviation is unknown, t-test for One Population Mean is be used.
Let = mean number of ticket a person have had in his life
The Null and Alternative Hypotheses are,
The t statistic is obtained using the formula,
Where,
Now,
The p-value is obtained from t distribution table for degree of freedom = n - 1 = 32 - 1 = 31 and significance level = 0.05
Since the P-value is greater than significance level = 0.05, the null hypothesis is not rejected. Hence there is no evidence to concluded that the mean number of tickets a person have had in his life is no equal to 5.