A mobile phone service provider wants to survey its customers to study privacy concerns and the sharing of their personal information. They call 5000 randomly selected phone numbers from a database containing the phone number of every customer. If someone selected doesn't answer, they'll attempt calling back up to 2 more times before giving up on reaching that person. They reach 350 customers with this strategy, and 60% of those reached say they are at least "somewhat concerned" about their personal information being shared without their knowledge or consent. Based on this information, and using a 95 percent confidence level, what is the critical value?

We are given that a mobile phone service provider wants to survey its customers to study privacy concerns and the sharing of their personal information.

They reach 350 customers with this strategy, and 60% of those reached say they are at least "somewhat concerned" about their personal information being shared without their knowledge or consent.

Let p = % of customers who said that they are at least "somewhat concerned" about their personal information being shared without their knowledge or consent.

The test statistics that would be used here is One-sample z test for proportions which means that we will use the z table for finding the critical value.

Also, it is given that a 95 percent confidence level is used; this means that the level of significance = 1 - Confidence level

= 1 - 0.95 = 0.05

Now, in the z table the critical value of z at 0.05 level of significance for one-tailed test is given as 1.645.

MrRoyal MrRoyal · Answer 2 · 2021-10-28T19:34:11+02:00

Critical values are simply the values cut-off from a region where the test statistic is unlikely to be;

The critical value is 1.645

The given parameters are:

[tex]\mathbf{p = 60\%}[/tex]

[tex]\mathbf{CL= 95\%}[/tex] --- the confidence level

We start by calculating the significance level

[tex]\mathbf{\alpha = 1 - CL}[/tex]

Substitute 95% for CL

[tex]\mathbf{\alpha = 1 - 95\%}[/tex]

Express 95% as decimal

[tex]\mathbf{\alpha = 1 - 0.95}[/tex]

[tex]\mathbf{\alpha = 0.05}[/tex]

At 0.05 significance level, the critical value is 1.645

So, we have:

[tex]\mathbf{t_c = 1.645}[/tex]

Hence, the critical value is 1.645