Question

1. A state’s Division of Motor Vehicles (DMV) claims that 60% of all teens pass their driving test on the
first attempt. An investigative reporter examines an SRS of the DMV records for 125 teens; 56 of them
passed the test on their first try. Is there convincing evidence at the α=0.01 significance level that the
DMV’s claim is lower?

2. In a recent year, 65% of first-year college students responding to a national survey identified “being
very well-off financially” as an important personal goal. A state university finds that 102 of an SRS of
200 of its first-year students say that this goal is important. Is there convincing evidence at
the α=0.05 significance level that the proportion of all first-year students at this university who think
being very well-off is important differs from the national value of 65%?

3. Every road has one at some point—construction zones that have much lower speed limits. To see if
drivers obey these lower speed limits, a police officer uses a radar gun to measure the speed (in miles
per hour, or mph) of a random sample of 10 drivers in a 25 mph construction zone. Here are the data:
27 33 32 21 30 30 29 25 27 34
Is there convincing evidence at the α=0.01 significance level that the average speed of drivers in this
construction zone is greater than the posted speed limit?

4. A school librarian purchases a novel for her library. The publisher claims that the book is written at a fifth-grade reading level, but the librarian suspects that the reading level is lower than that. The librarian selects a random sample of 45 pages and uses a standard readability test to assess the reading level of each page. The mean reading level of these pages is 4.8 with a standard deviation of 0.6. Do these data give convincing evidence at the α=0.01 significance level that the average reading level of this novel is less than 5?

Answer 1

1)

Answer:

Given that:

A state’s Division of Motor Vehicles (DMV) claims that 60% of all teens pass their driving test on the
first attempt. An investigative reporter examines an SRS of the DMV records for 125 teens; 56 of them
passed the test on their first try.

Null and alternative hypothesis will be

For and the critical value for two tailed test is

Test statistic

Decision:

Since it is observed that is is concluded that the null hypothesisi is rejected

Conclusion:

There is enough evidence that the DMV's claim is in correct