Question

Assume a media agency reports that it takes television streaming service subscribers in the United States an average of 6.24 days to watch the entire first season of a television series, with a standard deviation of 3.80 days. Suppose Elizabeth, an analyst for an online television and movie streaming service company, wants to determine if her company's customers exhibit similar viewing rates for their series offerings.

She formulated the null hypothesis ?0:?=6.24 daysH0:μ=6.24 days and the alternative ?1:?≠6.24 daysH1:μ≠6.24 days, where ?μ is the mean number of days that it takes for customers to watch the first season of a series. She conducted a one-sample ?-z-test based on data collected from a simple random sample of 850 customers who watched the first season of a television series from the company database of over 20,000 customers that qualified. She assumed that that the population standard deviation is ?=3.80 days.σ=3.80 days.

She compiled the summary statistics shown in the table.

Sample size	Sample mean	Standard error
?n	?⎯⎯⎯x¯	SE
850	6.11	0.13

Compute the ?-valueP-value for Elizabeth's hypothesis test directly using a normalcdf function on a TI calculator or software. You may find some software manuals helpful. Provide your answer with precision to four decimal places. Avoid rounding until the final step.

P-value =?

Select the accurate statement regarding Elizabeth's test decision if she tests at a significance level of ?=0.05α=0.05.

a.Elizabeth should fail to reject the null hypothesis because the ?-valueP-value is less than the value, ?=0.05α=0.05.

b.Elizabeth should reject the null hypothesis because the ?-valueP-value is less than the value, ?=0.05α=0.05.

c.Elizabeth should reject the null hypothesis because the ?-valueP-value is greater than the value, ?=0.05α=0.05.

d.Elizabeth should fail to reject the null hypothesis because the ?-valueP-value is greater than the value, ?2=0.025α2=0.025.

e.Elizabeth should fail to reject the null hypothesis because the ?-valueP-value is greater than the value, ?=0.05α=0.05.

Answer 1

The statistical software output for this problem is:

One sample Z summary hypothesis test: u Mean of population H4 = 6.24 HA1=6.24 Standard deviation = 3.8 Hypothesis test results: Mean Sample Mean Std. Err. Z-Stat 850 6.11 0.13033892 -0.99739967 P-value 0.3186

From above output:

P - value = 0.3186

Conclusion: Elizabeth should fail to reject the null hypothesis because the ?-valueP-value is greater than the value, ?=0.05

Option E is correct.