diff --git a/Lib/test/pythoninfo.py b/Lib/test/pythoninfo.py
@@ -529,6 +529,8 @@ def collect_resource(info_add):
         value = resource.getrlimit(key)
         info_add('resource.%s' % name, value)
 
+    call_func(info_add, 'resource.pagesize', resource, 'getpagesize')
+
 
 def collect_test_socket(info_add):
     try:

diff --git a/Lib/test/test_tarfile.py b/Lib/test/test_tarfile.py
@@ -973,16 +973,21 @@ def test_sparse_file_10(self):
     def _fs_supports_holes():
         # Return True if the platform knows the st_blocks stat attribute and
         # uses st_blocks units of 512 bytes, and if the filesystem is able to
-        # store holes in files.
+        # store holes of 4 KiB in files.
+        #
+        # The function returns False if page size is larger than 4 KiB.
+        # For example, ppc64 uses pages of 64 KiB.
         if sys.platform.startswith("linux"):
             # Linux evidentially has 512 byte st_blocks units.
             name = os.path.join(TEMPDIR, "sparse-test")
             with open(name, "wb") as fobj:
+                # Seek to "punch a hole" of 4 KiB
                 fobj.seek(4096)
+                fobj.write(b'x' * 4096)
                 fobj.truncate()
             s = os.stat(name)
             support.unlink(name)
-            return s.st_blocks == 0
+            return (s.st_blocks * 512 < s.st_size)
         else:
             return False
 

diff --git a/Misc/NEWS.d/next/Tests/2019-01-18-12-19-19.bpo-35772.sGBbsn.rst b/Misc/NEWS.d/next/Tests/2019-01-18-12-19-19.bpo-35772.sGBbsn.rst
@@ -0,0 +1,6 @@
+Fix sparse file tests of test_tarfile on ppc64 with the tmpfs filesystem. Fix
+the function testing if the filesystem supports sparse files: create a file
+which contains data and "holes", instead of creating a file which contains no
+data. tmpfs effective block size is a page size (tmpfs lives in the page cache).
+RHEL uses 64 KiB pages on aarch64, ppc64, ppc64le, only s390x and x86_64 use 4
+KiB pages, whereas the test punch holes of 4 KiB.