The distribution of heights of 6-year-old girls is approximately normally distributed with a mean of 46.0 inches and a standard
deviation of 2.7 inches. Aaliyah is 6 years old, and her height is 0.96 standard deviation above the mean. Her friend Jayne is also 6 years old and is at the 93rd percentile of the height distribution. At what percentile is Aaliyah’s height, and how does her height compare to Jayne’s height?
1 answer:
Answer:
Aaliyah's height is the 84th percentile and the relationship that there exists between Aaliyah's height and between Jayne's height is that Aaliyah's height is less than Jayne's height.
Step-by-step explanation:
Below we can observe the empirical rule with a mean of 46.0 inches and a standard deviation of 2.7 inches. We have that 48.7 inches represents one standard deviation above the mean, so, we can consider that Aaliyah's height is the 84th percentile. On the other side, Jayne's height is the 93rd percentile of the height distribution. Therefore, the relationship that there exists between Aaliyah's height and between Jayne's height is that Aaliyah's height is less than Jayne's height.
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Answer:
a) Failed to reject the null hypothesis (P-value=0.09).
b) The 95% CI for the difference in proportions is:
Step-by-step explanation:
a) We have to perform a hypothesis test for the difference of proportions.
The null and alternative hypothesis are:
The significance level is 0.05.
The proportion of the passenger cars owners is:
The proportion of commercial truck owners is:
The weigthed average p is
The estimated standard deviation is
We can calculate the z-value as:
The P-value for z=-1.362 is P=0.0866.
The P-value (0.09) is greater than the significance level (0.05), so it failed to reject the null hypothesis. There is no enough evidence to prove that commercial trucks owners violate laws requiring front license plates at a higher rate than owners of passenger cars.
b) We can construct a 95% CI, according to the significance level of 0.05.
The z-value for this CI is 1.96.
We have to recalculate the standard deviation:
The lower limit is then:
The upper limit is:
The 95% CI for the difference in proportions is:
In this case, we can conclude that the difference between the proportions, with 95% confidence, can still be equal or greater than zero, meaning that it is possible passenger car owners violate laws more than truck owners.