My instructions said:

If that doesn't work, you need to find out in which directory the ping executable lives, and put the name of that directory into $ENV{PATH} instead.

So, did you try the following:

$ENV{PATH} = '/sbin';
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at the top of your script?

If so, what do you mean by Does not work ? In what way does it not work? Does it report all hosts as reachable ? All hosts as unreachable? Does it claim that the ancient gods of Egypt will conquer the world tomorrow when you know that their uprising is scheduled for next year?

yes, I tried that - I get the same result when I run the code:

Insecure dependency in connect while running with -T switch at /usr/libdata/perl5/Net/Ping.pm line 914.

I ran your code from the command line and it did not throw any error, and it even correctly reported all three hosts as up. But then I got the idea that maybe there is a file ship.cfg in your current directory (which you did not mention but which I should have caught sooner). Taint mode regards input from local files as tainted (see perldoc perlsec or the perldoc online page). So you will need to untaint that data manually. I chose the sledgehammer approach to untainting:

if ( -e "ship.cfg" ) {
        open (CFGFILE, "<", "ship.cfg") || die;
        @hosts=<CFGFILE>;
        close (CFGFILE);
        # untaint all data from ship.cfg
        @hosts = map { /^(.*)$/ and $1 } @hosts;
} else {
        # Enter your hosts here...
        @hosts = qw/host1 host2 host3 aliens/;
}
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But I would recommend hardcoding all hosts in the script instead, as that will be much more secure than reading in a file and pinging every host named in that file.