Set up a mean hypothesis test by choosing a one-sample or paired t-procedure and matching parameter, equality, direction, and subtraction order to the claim.
A top-100, 7.0-rated ten)nis pro wishes to compare a new racket against his current model. He is interested in whether his hitting speed with the new racket is different from that with his old racket. He strings the new racket with the same type of strings at 60 pounds tension that he uses on his old racket. From past testing, the tennis pro knows that the average forehand crosscourt volley with his old racket is 82 miles per hour (mph). On an indoor court, using a ball machine set at 70 mph, which is the same speed he had his old racket tested against, he takes 47 swings with the new racket. (Assume that swings are independent of each other.) An associate with a speed gun records an average of 83.5 mph with a standard deviation of 3.4 mph. At the 0.01 level of significance, complete the appropriate inference procedure to determine if there is convincing statistical evidence that his mean hitting speed with the new racket is different from that with his old racket.
Identify the appropriate inference procedure.
According to a 2017 national survey in Country B, the mean number of bedrooms in newly built houses was 2.9. Rodney, a researcher, believes the mean number of bedrooms in newly built houses in the country was different in 2024 than it was in 2017. To investigate his belief, he took a large random sample of newly built houses in Country B in 2024 and recorded the number of bedrooms in each house. The distribution of the number of bedrooms for the sampled houses is summarized in the table.
Distribution of the Number of Bedrooms for the Houses Sampled in 2024
Rodney will use a one-sample t-test for a population mean to test his belief.
In the context of Rodney's investigation, state the hypotheses for the test.