Question

What is the p-value? Interpret it. A recent national survey found that high school students watched an average of 6.8 DVDs per month with a population standard deviation of 0.5 hours. The distribution of times follows the normal distribution. A random sample of 36 college students revealed that the mean number of DVDs watched last month was 6.2. At the .05 significance level, can we conclude that college students watch fewer DVDs a month than high school students?

Answer 1

We conclude that college students watch fewer DVDs a month than high school students.

Explanation:

We are given that a recent national survey found that high school students watched an average of 6.8 DVDs per month with a population standard deviation of 0.5 hours.

A random sample of 36 college students revealed that the mean number of DVDs watched last month was 6.2.

Let
`\mu` = average DVDs a month watched by college students.

So, Null Hypothesis,
`H_0` :
`\mu`
`\geq` 6.8 DVDs per month {means that college students watch greater or equal DVDs a month than high school students}

Alternate Hypothesis,
`H_A` :
`\mu` < 6.8 DVDs per month {means that college students watch fewer DVDs a month than high school students}

The test statistics that would be used here One-sample z test statistics as we know about the population standard deviation;

T.S. =
`(\bar X-\mu)/((\sigma)/(√(n) ) )` ~ N(0,1)

where,
`\bar X` = sample mean number of DVDs watched last month = 6.2

s = population standard deviation = 0.5 hours

n = sample of college students = 36

So, the test statistics =
`(6.2-6.8)/((0.5)/(√(36) ) )`

= -7.2

The value of z test statistics is -7.2.

Now, at 0.05 significance level the z table gives critical value of -1.645 for left-tailed test.

Since our test statistic is less than the critical value of z as -7.1 < -1.645, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that college students watch fewer DVDs a month than high school students.

Also, P-value is the probability of obtaining results which are as extreme as related to observed results or in other words; it is the exact region where or tests statistics lies.