Test d'ipotesi
Ciao ragazzi!
Mi trovo ad aver a che fare con questi due seguenti test d'ipotesi. In particolare, vorrei avere una chiarificazione a riguardo la differenza tra ipotesi nulla ed ipotesi alternativa. Cioè l'ipotesi nulla è quella che risulta più probabile dalla verifica o quella che penso sarà la più probabile va messa in ipotesi alternativa?
Per quanto riguarda questi due seguenti test , nel primo credo che : Ipotesi alternativa: M>24 e Ipotesi nulla: M<24
il secondo invece: Ipotesi nulla : M>480 Ipotesi alternativa: M<480 .
Il testo dei due è il seguente :
Test 1
Willco is a manufacturer in a mature cyclical industry. Considering a sample of the last 6
years, its average yearly net income is 30 million dollars with a standard deviation of 10 million
(data referring to a sample n=6 observations). Management claims that Willco's performance
during the most recent cycle results from new approaches and that the pro tability expectations
of prior cycles, corresponding to 24 million dollars on average, can be considered surpassed.
a) Formulate null and alternative hypothesis consistent with testing Willco's management's
claim.
b) Assuming Willco's net income is approximately normally distributed, determine whether
or not to reject the null hypothesis at the 0.05 signi cance level.
Test 2
Simona has to fly to New York for a job meeting. She has been there already 7 times in the past, and on average her flights were 483 minutes (=8 hours and 3 minutes) long. We assume a normal distribution for the length of the flight with variance = 30 min2. Simona obtains the information from the airlines website that her flight will take 8 hours (=480 minutes) and,
therefore, she uploads music on her Ipod lasting 8 hours. She wants to test whether the music will be enough for the flight.
a) Which are the null and the alternative hypothesis?
b) Which is the test of hypothesis that we consider for this problem?
c) What can we tell Simona? Will be the music enough at level = 0:05?
Grazie in anticipo ragazzi!!
Mi trovo ad aver a che fare con questi due seguenti test d'ipotesi. In particolare, vorrei avere una chiarificazione a riguardo la differenza tra ipotesi nulla ed ipotesi alternativa. Cioè l'ipotesi nulla è quella che risulta più probabile dalla verifica o quella che penso sarà la più probabile va messa in ipotesi alternativa?
Per quanto riguarda questi due seguenti test , nel primo credo che : Ipotesi alternativa: M>24 e Ipotesi nulla: M<24
il secondo invece: Ipotesi nulla : M>480 Ipotesi alternativa: M<480 .
Il testo dei due è il seguente :
Test 1
Willco is a manufacturer in a mature cyclical industry. Considering a sample of the last 6
years, its average yearly net income is 30 million dollars with a standard deviation of 10 million
(data referring to a sample n=6 observations). Management claims that Willco's performance
during the most recent cycle results from new approaches and that the pro tability expectations
of prior cycles, corresponding to 24 million dollars on average, can be considered surpassed.
a) Formulate null and alternative hypothesis consistent with testing Willco's management's
claim.
b) Assuming Willco's net income is approximately normally distributed, determine whether
or not to reject the null hypothesis at the 0.05 signi cance level.
Test 2
Simona has to fly to New York for a job meeting. She has been there already 7 times in the past, and on average her flights were 483 minutes (=8 hours and 3 minutes) long. We assume a normal distribution for the length of the flight with variance = 30 min2. Simona obtains the information from the airlines website that her flight will take 8 hours (=480 minutes) and,
therefore, she uploads music on her Ipod lasting 8 hours. She wants to test whether the music will be enough for the flight.
a) Which are the null and the alternative hypothesis?
b) Which is the test of hypothesis that we consider for this problem?
c) What can we tell Simona? Will be the music enough at level = 0:05?
Grazie in anticipo ragazzi!!
Risposte
A fi rm has to decide whether to change its manufacturing process or not. The actual manufacturing process produces on average 80 pieces per hour. The new manufacturing process should allow for producing on average more than 100 pieces per hour. The fi rm wants therefore verify whether its expectation on the new manufacturing process are reasonable. Which are the null and the alternative hypotheses that the rm wants to compare? Which are the fi rst type and the second type errors of the corresponding test of hypothesis?
A bank wants to evaluate the percentage of its clients who are interested in a new home banking service. Taking into account costs and pro ts due to this service, the bank establishes that the home banking service is pro table if the percentage of clients interested in the service is at least 40%. Which are the null and the alternative hypotheses about that the bank wants to verify at level = 0:01? Which are the rst type and the second type errors of the corresponding test of hypothesis?
Io avevo pensato: il primo test: M=40 alternative: M>40
per il secondo: M<100 alternative: M>100
A bank wants to evaluate the percentage of its clients who are interested in a new home banking service. Taking into account costs and pro ts due to this service, the bank establishes that the home banking service is pro table if the percentage of clients interested in the service is at least 40%. Which are the null and the alternative hypotheses about that the bank wants to verify at level = 0:01? Which are the rst type and the second type errors of the corresponding test of hypothesis?
Io avevo pensato: il primo test: M=40 alternative: M>40
per il secondo: M<100 alternative: M>100
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