6. The market research firm Salary.com reported that the mean annual earnings of all family practitioners in the United States was $178,258. A random sam- ple of 55 family practitioners in Los Angeles that month had a mean earning of X = $192, 140 with a standard deviation of $42,387. Do the data provide sufficient evidence to conclude that the mean salary for family practitioners in Los Angeles is greater than the national average? (a) State the null and alternative hypothesis. (b) Compute the value of the t-statistics. How many degrees of freedom are there? (c) State your conclusion. Use = 0.05 level of significance. 7. (BONUS) According to Secure List, 71.8% of all emails sent is spam. A system manager at a large corporation believes that the percentage at his company may be 80%. He examines a random sample of 500 emails received at an email server and finds that 382 of the messages are spam. (a) State the appropriate null and alternative hypothesis. (b) Compute the test statistics. (c) Use = 0.05 level of significance, can you conclude that the percentage of emails that are spam differs from 80%? (d) Use = 0.1 level of significance, can you conclude that the percentage of emails that are spam differs from 80%?