4. co KLLTLUJIUI III USed a Sample of IndiMiduals to rate the purchase potential of a particular product before and after the individuals saw a new television commercial about the product. The purchase potential ratings were based on a 0 to 10 scale, with higher values indicatinc higher purchase potential. The null hypothesis stated that the mean rating "after" would be less than or equal to the mean rating "before." Rejection of this hypothesis would show that the commercial improved the mean purchase potential rating. Use a= 0.05 and the following da test the hypothesis and comment on the value of the commercial. Purchase Rating Individual After Before 6 2 6 4. 4 3 3 9 8. 7 6. State the null and alternative hypotheses. (Use u = mean rating after - mean rating before.) O H: = 0 O H: H>0 05 Pr:H O O Hi H #0 Hi4 = 0 Calculate the value of the test statistic. (Round your answer to three decimal places.) Calculate the p-value. (Round your answer to four decimal places.) p-value = State your conclusion. O Do not Reject H There is sufficient evidence to conclude that seeing the commercial improves the mean potential to purchase. O Do not reject H There is insufficient evidence to conclude that seeing the commercial improves the mean potential to purchase. O Reject H There is insufficient evidence to conclude that seeing the commercial improves the mean potential to purchase.
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
Answer:
from the above information
mean= =0.625
standard deviation ==1.302
sample size = n =8
the hypothesis is
H0 :
H1 :
The test statistic is
t=
t=
t=1.357
the value of test statistic t=1.357
p vale
by using p value table of t distribution with test statistic t=1.357 and degree of freedom =n-1=8-1=7
p value =0.1385
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