1. A manufacturer makes steel rods that are suppose to have a mean length of 50cm. A retailer suspects the bars are running short. A sample of 41 bars is taken and their mean length is determined to be 51 cm with a sample standard deviation of 3.6. Test the claim the mean is less than50 cm at the .01 level of significance (use t)

2. A test of sobriety involves measuring the subject's motor skills. Twenty randomly selected sober subjects produced a mean score of 41 with a known population standard deviation of 3.7. At the .01 level of significance test the claim the true mean score for all sober subjects is equal to 35. Use the .05 level and the z.

3. Has the proportion of Facebook accounts decreased worldwide? Many young adults believe that that is the case because several other social media platforms now taking center stage. In 2020 a report claimed 59% of social media users use Facebook. Suppose you conducted a survey of 48 people showed 23 of them still have a Facebook account. Use the .05 level of significance to determine whether the proportion of social media users who have a Facebook account is lower than 59%