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Answer:
We conclude that those celebrating Valentine's Day spend more than an average of $125 on gifts.
Step-by-step explanation:
We are given that Hallmark would like to test the hypothesis that those celebrating Valentine's Day will spend more than an average of $125 on gifts.
A random sample of 18 people celebrating Valentine's Day spent an average of $148.50 with a standard deviation of $34.90.
<u><em>Let </em></u><u><em> = average amount spent on gifts celebrating Valentine's Day</em></u>
So, Null Hypothesis, :
$125 {means that those celebrating Valentine's Day spend less than or equal to an average of $125 on gifts}
Alternate Hypothesis, :
> $125 {means that those celebrating Valentine's Day spend more than an average of $125 on gifts}
The test statistics that will be used here is <u>One-sample t test statistics</u> as we don't know about population standard deviation;
T.S. = ~
where, = sample average amount spent = $148.50
s = sample standard deviation = $34.90
n = sample of people = 18
So, <u>test statistics</u> = ~
= 2.857
The value of the sample test statistics is 2.857.
<u>Now, P-value of the test statistics is given by the following formula;</u>
P-value = P( > 2.857) = <u>0.0056</u>
Because in the t table the critical value of 2.857 at 17 degree of freedom will lie between P = 1% and P = 0.5%.
Now, since P-value of test statistics is less than the level of significance as 0.01 > 0.0056, so we sufficient evidence to reject our null hypothesis.
Therefore, we conclude that those celebrating Valentine's Day spend more than an average of $125 on gifts.