Question

1. A marketing analyst is researching how to increase organic growth to company websites. During their research, the marketing analyst states the average number of words on a website's first page is longer than 1500 words.
If we would like to test the marketing analyst's claim with a hypothesis test using a significance level of α=0.025 , which of the following choices are true?

Select the correct answer below:

There is a 2.5% chance we will conclude μ>1500, but is in fact μ=1500.

There is a 2.5% chance of rejecting the null hypothesis.

There is a 2.5% chance we will conclude μ=1500, but is in fact μ>1500.

There is a 2.5% chance that μ>1500.

2. The pages per book in a library are normally distributed with a population standard deviation of 45 pages and an unknown population mean. A random sample of 15 books is taken and results in a sample mean of 305 pages.

What is the correct interpretation of the 99% confidence interval?

Select the correct answer below:

We estimate that 99% of the books in the library have between 275 and 335 pages.

We estimate with 99% confidence that the sample mean is between 275 and 335 pages.

We estimate with 99% confidence that the true population mean is between 275 and 335 pages.

Answer 1

Solution:

1)

Given:

Null hypothesis:

Alternative hypothesis:

= 0.025 = 2.5%

First need to know about the significance level:

The fixed significance level only determines whether the sample mean is significant or not significant, when the null hypothesis is true.

Therefore, correct statement is,

Here is a 2.5% chance we will conclude μ>1500, but is in fact μ=1500.

2.

Sample mean = = 305

Population SD= = 45

Sample size = n = 15

The critical value for α=0.01 is zc ​= z_1−α/2 ​= 2.576. Using excel function, =ABS(NORMSINV(0.01/2))

Therefore 95% confidence interval for population mean is,

( 275 , 335)

Hence, we estimate with 99% confidence that the true population mean is between 275 and 335 pages.

Done