[1]
An earlier study claims that U.S. adults spend an average of 114 minutes with
their families per day. A recently taken
sample of 25 adults showed that they spend an average of 109 minutes per day
with their families. The sample standard
deviation is 11 minutes. Assume that the
time spent by adults with their families has an approximate normal
distribution. We wish to test whether the mean time spent currently by all
adults with their families is less than 114 minutes a day.

1. Set
   up the null and alternative hypotheses.

2. Select
   the distribution to use. Explain briefly
   why you selected it.

3. Using
   the 2.5% significance level, determine the rejection and non-rejection regions
   based on your hypotheses in a). State
   the critical value.

4. Calculate
   the value of the test statistic.

5. Does the sample information support that the
   mean time spent currently by all adults with their families is less than 114
   minutes a day? Explain your conclusion
   in words.

   Since the test statistics
   value is smaller than lower critical value so we will reject the null
   hypothesis. The sample information support that the mean time spent currently
   by all adults with their families is less than 114 minutes a day.

[2] In recent years, the Town of New Port
experienced an arrest rate of 25% for robberies (based on FBI data). The new sheriff complies records showing that
among 30 recent robberies, the arrest rate is 30%, so she claims that her
arrest rate is greater than the 25% rate in the past. We want to test if there is sufficient
evidence to support her claim.

1. Set
   up the null and alternative hypotheses, and perform the hypothesis test with a
   significance level of 0.05.

2. .5in;’=”” list=”” none;=”” lfo1;=”” l0=””>Does
   the sample information support that her claim that the arrest rate is greater
   than 25%? Explain your conclusion in
   words.

[3] A survey conducted by the American
Automobile Association showed that a family of four spends an average of
$215.60 per day while on vacation.
Suppose a sample of 64 families of four vacationing at Niagara Falls
resulted in a sample mean of $252.45 per day and a sample standard deviation of
$74.50. We shall use a 0.05 significance
level to test the claim that a family of four will spend more money, on
average, when vacationing at Niagara Falls per day than the average amount for
a family of four claimed by the American Automobile Association.

1. Set
   up the null and alternative hypotheses, and perform the hypothesis test.

2. .5in;’=”” list=”” none;=”” lfo4;=”” l1=””>Based
   on results of the hypothesis test in part a), does it appear that the
   population mean amount spent per day by families visiting Niagara Falls is more
   than the mean amount per day for a family of four reported by the American
   Automobile Association? Explain.

[4] In the case of Casteneda v. Partida, 1977, it was found that during
a period of 11 years in Hilda County, Texas, 870 people were selected for grand
jury duty, and 39% of them were Americans of Mexican ancestry. Among the people eligible for grand jury
duty, 79.1% were Americans of Mexican ancestry.
We shall use a 0.02 significance level to test the claim that the
selection process is biased against Americans of Mexican ancestry.

1. Set
   up the null and alternative hypotheses, and perform the hypothesis test.

2. Does
   the jury selection system appear to be fair?

   [5] A bakery in my neighborhood produces
   loaves of bread with “1 pound” written on the label. Weights of randomly selected sampled loaves
   from today’s production were recorded below:

1. If
   you are to perform a hypothesis test to test the claim on the label that the
   mean weight of the entire loaves of bread production is more than “1 pound,”
   what distribution are you going to apply and explain why?

2. If an average weight is less than or equal
   to “1 pound,” then customers think that the bakery is taking advantage of its weight. When customers find out its actual weight,
   they might certainly complain about it.
   Use a 0.05 significance level to test the claim that the mean weight of
   the entire loaves of bread production is more than “1 pound.”

3. Do you think that the bakery is correct in
   its label claim?

[6]
On January 7, 2000, the Gallup Organization released the results of a poll
comparing lifestyles of today with that yesteryear. Then poll results were based in telephone
interviews with a randomly selected national sample of 1,031 adults, 18 years
and older, conducted December 20-21, 1999.
One question asked if the respondent had vacationed for six days or
longer within the last 12 months.
Suppose that we will attempt to use the poll’s results to justify the claim
that more than 40 percent of U.S. adults have vacationed for six days or longer
within the last 12 months. The poll
actually found that 42 percent of the respondents had done so. Would you conclude that more than 40 percent
of U.S. adults have vacationed for six days or longer within the last 12
months? Explain.

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