9. The relationship between confidence intervals and hypothesis testing Aa Aa In an effort to better manage his inventory levels, the owner of two steak and seafood restaurants, both located in the same city, hires a statistician to conduct a statistical study. The owner is interested in whether the restaurant located on the south side sells more salmon fillets per night than the restaurant located on the north side of the city. The statistician selects a random sample of size n1 = 35 nights that the southside restaurant is open. For each night in the sample, she collects data on the number of salmon fillets sold at the southside location and computes the sample mean M1 = 34.81 and the sample variance s = 28. Likewise, she selects a random sample of size n2 = 32 nights that the northside restaurant is open. For each night in the sample, she collects data on the number of salmon fillets sold at the northside location and computes the sample mean M2 = 39.26 and the sample variance s3 = 27. %3D The statistician checks and concludes that the data satisfy the required assumptions for the independent-measures t test. Then she computes the 95% confidence interval for estimating the difference between the mean number of salmon fillets sold per night at the southside restaurant and the mean number of salmon fillets sold per night at the northside restaurant. This 95% confidence interval is -4.45 ± 2.5624 salmon fillets. If she were to formulate null and alternative hypotheses as Ho: µ1 – P2 = 0, H1: µ1 – P2 # 0 and conduct a hypothesis test in the computed a significant difference between the mean nightly sales of salmon with a = .05, the null hypothesis rejected based on the result that a difference of zero interval. Hence, she would conclude that there fillets between the two restaurants.
9. The relationship between confidence intervals and hypothesis testing Aa Aa In an effort to better manage his inventory levels, the owner of two steak and seafood restaurants, both located in the same city, hires a statistician to conduct a statistical study. The owner is interested in whether the restaurant located on the south side sells more salmon fillets per night than the restaurant located on the north side of the city. The statistician selects a random sample of size n1 = 35 nights that the southside restaurant is open. For each night in the sample, she collects data on the number of salmon fillets sold at the southside location and computes the sample mean M1 = 34.81 and the sample variance s = 28. Likewise, she selects a random sample of size n2 = 32 nights that the northside restaurant is open. For each night in the sample, she collects data on the number of salmon fillets sold at the northside location and computes the sample mean M2 = 39.26 and the sample variance s3 = 27. %3D The statistician checks and concludes that the data satisfy the required assumptions for the independent-measures t test. Then she computes the 95% confidence interval for estimating the difference between the mean number of salmon fillets sold per night at the southside restaurant and the mean number of salmon fillets sold per night at the northside restaurant. This 95% confidence interval is -4.45 ± 2.5624 salmon fillets. If she were to formulate null and alternative hypotheses as Ho: µ1 – P2 = 0, H1: µ1 – P2 # 0 and conduct a hypothesis test in the computed a significant difference between the mean nightly sales of salmon with a = .05, the null hypothesis rejected based on the result that a difference of zero interval. Hence, she would conclude that there fillets between the two restaurants.
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Transcribed Image Text:9. The relationship between confidence intervals and hypothesis testing
Aa Aa
In an effort to better manage his inventory levels, the owner of two steak and seafood restaurants, both located in the same
city, hires a statistician to conduct a statistical study. The owner is interested in whether the restaurant located on the south side
sells more salmon fillets per night than the restaurant located on the north side of the city.
The statistician selects a random sample of size n1 = 35 nights that the southside restaurant is open. For each night in the
sample, she collects data on the number of salmon fillets sold at the southside location and computes the sample mean M1
34.81 and the sample variance s = 28. Likewise, she selects a random sample of size n2
= 32 nights that the northside
%3D
restaurant is open. For each night in the sample, she collects data on the number of salmon fillets sold at the northside location
and computes the sample mean M2
39.26 and the sample variance s, = 27.
The statistician checks and concludes that the data satisfy the required assumptions for the independent-measures t test. Then
she computes the 95% confidence interval for estimating the difference between the mean number of salmon fillets sold per
night at the southside restaurant and the mean number of salmon fillets sold per night at the northside restaurant. This 95%
confidence interval is -4.45 ± 2.5624 salmon fillets.
If she were to formulate null and alternative hypotheses as Ho: µ1 – P2 = 0, H1: µ1 - P2 # 0 and conduct a hypothesis test
in the computed
a significant difference between the mean nightly sales of salmon
with a =
.05, the null hypothesis
rejected based on the result that a difference of zero
interval. Hence, she would conclude that there
fillets between the two restaurants.
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