jenna eats dinner at a restaurant. her bill is 14.50. jenna pays her bill and leaves a tip. write an inequality to represent the
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Answer:
he can expect to lose 0.5$
Step-by-step explanation:
To solve this problem we must calculate the expected value of the game.
If x is a discrete random variable that represents the gain obtained when rolling a dice, then the expected value E is:
When throwing a dice the possible values are:
x: 1→ -$9; 2→ $4; 3→ -$9; 4→ $8; 5→ -$9; 6→ $12
The probability of obtaining any of these numbers is:
The gain when obtaining an even number is twice the number.
The loss to get an odd number is $ 9
So the expected gain is:
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.