Question

A marketing researcher wants to estimate the mean amount spent ($) on Amazon.com by Amazon Prime member shoppers. Suppose a random sample of 100 Amazon Prime member shoppers who recently made a purchase on Amazon.com yielded a mean amount spent of $1,500 and a standard deviation of $200. Is there evidence that the population mean amount spent on Amazon.com by Prime member shoppers is different from $1,475? (Use a 5% level of significance.) Also, suppose that the p-value is 0.2142.

A: We fail to reject the null hypothesis since t-stat = 1.25 is smaller than the critical value = 1.98.

B: We fail to reject the null hypothesis since the provided p-value < 0.05.

C: Both B & C

D: We reject the null hypothesis since the t-stat = 1.25 is less than the critical value 2.01

Answer 1

We fail to reject the null hypothesis since t-stat = 1.25 is smaller than the critical value = 1.98.

Explanation:

We are given that a random sample of 100 Amazon Prime member shoppers who recently made a purchase on Amazon.com yielded a mean amount spent of $1,500 and a standard deviation of $200.

We have check that is there evidence that the population mean amount spent on Amazon.com by Prime member shoppers is different from $1,475.

Let
`\mu` = population mean amount spent on Amazon.com by Prime member shoppers.

SO, Null Hypothesis,
`H_0` :
`\mu` = $1,475 {means that the population mean amount spent on Amazon.com by Prime member shoppers is equal to $1,475}

Alternate Hypothesis,
`H_A` :
`\mu`
`\\eq` $1,475 {means that the population mean amount spent on Amazon.com by Prime member shoppers is different from $1,475}

The test statistics that will be used here is One-sample t test statistics as we don't know about the population standard deviation;

T.S. =
`(\bar X -\mu)/((s)/(√(n) ) )` ~
`t_n_-_1`

where,
`\bar X` = sample mean amount spent = $1,500

s = sample standard deviation = $200

n = sample of Amazon Prime member shoppers = 100

So, test statistics =
`(1,500-1,475)/((200)/(√(100) ) )` ~
`t_9_9`

= 1.25

Hence, the value of test statistics is 1.25.

Now at 5% significance level, the t table gives critical values between -1.98 and 1.98 at 99 degree of freedom for two-tailed test. Since our test statistics lies within the range of the critical values of t, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region and due to this we fail to reject the null hypothesis.

Therefore, we conclude that the population mean amount spent on Amazon.com by Prime member shoppers is equal to $1,475.