A variety of stores offer loyalty programs. Participating shoppers swipe a bar-coded tag at the register when checking out and receive discounts on certain purchases. Stores benefit by gleaning information about shopping habits and hope to encourage shoppers to spend more. A typical Saturday morning shopper who does not participate in this program spends $150 on her or his order. In a sample of 80 shoppers participating in the loyalty program, each shopper spent $160 on average during a recent Saturday, with standard deviation s = $40. Is this statistical proof that the shoppers participating in the loyalty program spend more on average than typical shoppers? (Assume that the data meet the sample size condition.) Complete parts a-d. (a) State the null and alternative hypotheses. Describe the parameters. Choose the correct answer below. O A. Ho: us$150 vs H: u>$150; u is the average spent by a shopper not in the program. O B. Ho: us$150 vs H,: u>$150; u is the average spent by a shopper in the loyalty program. OC. Ho: u2$150 vs H: u<$150; µ is the average spent by a shopper in the loyalty program. O D. Ho: µ2$150 vs H: u<$150; u is the average spent by a shopper not in the program. (b) Describe the Type I and Type Il errors. Choose the correct answer below. O A. Concluding that loyal shoppers do not spend more when in fact they do is a Type I error. Concluding that loyal shoppers spend more when in fact they do not is a Type Il error. O B. Concluding that loyal shoppers spend more when in fact they do not is a Type I error. Concluding that loyal shoppers do not spend more when in fact they do is a Type Il error. Oc. Concluding that loyal shoppers spend more when in fact they do not is a Type I error. Concluding that loyal shoppers do not spend more and they do not is a Type Il error. O D. Concluding that loyal shoppers spend more and they do is a Type I error. Concluding that loyal shoppers do not spend more when in fact they do is a Type Il error. (c) How large could the kurtosis be without violating the CLT condition? K, must be less than
A variety of stores offer loyalty programs. Participating shoppers swipe a bar-coded tag at the register when checking out and receive discounts on certain purchases. Stores benefit by gleaning information about shopping habits and hope to encourage shoppers to spend more. A typical Saturday morning shopper who does not participate in this program spends $150 on her or his order. In a sample of 80 shoppers participating in the loyalty program, each shopper spent $160 on average during a recent Saturday, with standard deviation s = $40. Is this statistical proof that the shoppers participating in the loyalty program spend more on average than typical shoppers? (Assume that the data meet the sample size condition.) Complete parts a-d. (a) State the null and alternative hypotheses. Describe the parameters. Choose the correct answer below. O A. Ho: us$150 vs H: u>$150; u is the average spent by a shopper not in the program. O B. Ho: us$150 vs H,: u>$150; u is the average spent by a shopper in the loyalty program. OC. Ho: u2$150 vs H: u<$150; µ is the average spent by a shopper in the loyalty program. O D. Ho: µ2$150 vs H: u<$150; u is the average spent by a shopper not in the program. (b) Describe the Type I and Type Il errors. Choose the correct answer below. O A. Concluding that loyal shoppers do not spend more when in fact they do is a Type I error. Concluding that loyal shoppers spend more when in fact they do not is a Type Il error. O B. Concluding that loyal shoppers spend more when in fact they do not is a Type I error. Concluding that loyal shoppers do not spend more when in fact they do is a Type Il error. Oc. Concluding that loyal shoppers spend more when in fact they do not is a Type I error. Concluding that loyal shoppers do not spend more and they do not is a Type Il error. O D. Concluding that loyal shoppers spend more and they do is a Type I error. Concluding that loyal shoppers do not spend more when in fact they do is a Type Il error. (c) How large could the kurtosis be without violating the CLT condition? K, must be less than
MATLAB: An Introduction with Applications
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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.
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Transcribed Image Text:A variety of stores offer loyalty programs. Participating shoppers swipe a bar-coded tag at the register when checking out and receive discounts on certain purchases. Stores benefit by gleaning information about shopping habits and hope to
encourage shoppers to spend more. A typical Saturday morning shopper who does not participate in this program spends $150 on her or his order. In a sample of 80 shoppers participating in the loyalty program, each shopper spent $160 on
average during a recent Saturday, with standard deviations = $40. Is this statistical proof that the shoppers participating in the loyalty program spend more on average than typical shoppers? (Assume that the data meet the sample size
condition.) Complete parts a-d.
.....
(a) State the null and alternative hypotheses. Describe the parameters. Choose the correct answer below.
O A. Ho: µs $150 vs Ha: µ> $150; µ is the average spent by a shopper not in the program.
B. Ho: µs $150 vs Hạ: µ> $150; µ is the average spent by a shopper in the loyalty program.
C. Ho: µ2 $150 vs Hại µ< $150; µ is the average spent by a shopper in the loyalty program.
D. Ho: µ2 $150 vs Hg: µ<$150; µ is the average spent by a shopper not in the program.
(b) Describe the Type I and Type IIl errors. Choose the correct answer below.
O A. Concluding that loyal shoppers do not spend more when in fact they do is a Type I error. Concluding that loyal shoppers spend more when in fact they do not is a Type Il error.
B. Concluding that loyal shoppers spend more when in fact they do not is a Type I error. Concluding that loyal shoppers do not spend more when in fact they do is a Type Il error.
C. Concluding that loyal shoppers spend more when in fact they do not is a Type I error. Concluding that loyal shoppers do not spend more and they do not is a Type Il error.
D. Concluding that loyal shoppers spend more and they do is a Type I error. Concluding that loyal shoppers do not spend more when in fact they do is a Type II error.
(c) How large could the kurtosis be without violating the CLT condition?
K, must be less than
(d) Find the p-value of the test. Do the data reject the null hypothesis if oa = 0.05?
p-value =
(Round to four decimal places as needed.)
Do the data reject the null hypothesis if a = 0.05? Choose the correct answer below.
A. Do not reject Ho. There is sufficient evidence that shoppers in the loyalty program spend more than $150 on average.
B. Do not reject Ho. There is not sufficient evidence that shoppers in the loyalty program spend more than $150 on average.
C. Reject Ho. There is not sufficient evidence that shoppers in the loyalty program spend more than $150 on average.
D. Reject Hn. There is sufficient evidence that shoppers in the loyalty program spend more than $150 on average.
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