SHOW WORK AND CALCULATIONS

1. Determine whether the hypothesis test for a claim: "at most 34% of all homeowners have a home security alarm" should be left, right or two tails test. Write the corresponding null and alternative hypotheses.

2. Determine the Critical Value for a left tailed test about the population mean at = 0.05 level of significance, based on a sample size of 13.

3. A medical investigation claims that the average number of infections per week at a hospital in Pennsylvania is not 19.1. A random sample of 32 weeks had a mean number of 17.7 infections, and a sample standard deviation is 3.8. Is there enough evidence to support the investigator's claim? Use a 10 % level of significance to test this claim. (Test the claim using critical value method)

4. A spokesperson for the National Association of Broadcasters claims that less than 80% of all satellite radio subscribers have a satellite radio receiver in their car. A survey of 501 satellite radio subscribers shows that 355 of them had a satellite receiver in their car. Test the spokesperson claim at a 1% level of significance.

(Use p-value method)