The shakers measures about 3'' tall. They appear to be in near mint unused condition as pictured.
Some information from the Naval History and Heritage Command includes the following:
U.S.S. Alabama (BB-60), 1942 - 1964
U.S.S. Alabama, a 35,000 ton South Dakota class battleship, was built at the Norfolk Navy Yard, Portsmouth, Virginia. Commissioned in August 1942, she operated along the United States East Coast in late 1942 and early 1943, and was then stationed in the North Atlantic to guard against the threat of raids by German heavy ships. Alabama was transferred to the Pacific in August 1943. During November of that year, she took part in the operation to capture the Gilbert Islands. In 1944, Alabama participated in taking the Marshalls, the Marianas and Leyte, the Battles of the Philippine Sea and Leyte Gulf, and raids on Japanese positions elsewhere in the Pacific.
Following overhaul and training in January - April 1945, the battleship rejoined the fleet for operations in the Western Pacific, including attacks on the Japanese home islands. She took part in the occupation of Japan and the return of Veterans to the United States in August - October 1945. USS Alabama decommissioned at the Puget Sound Navy Yard, Bremerton, Washington, in January 1947 and remained in reserve until struck from the Naval Vessel Register in June 1962. Two years later, she was turned over to the State of Alabama. Since September 1964, Alabama has been berthed at Mobile, Alabama, as a memorial to those who served and sacrificed during World War II.